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AUTHOR: 


FOWLER,  THOMAS 


TITLE: 


ELEMENTS  OF 
DEDUCTIVE  LOGIC 

PLACE: 

OXFORD 

DA  TE : 

1892 


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>Fowler,  Thomas,  ilfb*:  1B3S- 1904,    .       ' 
r'^  •*>»    The  elements  of  deductive  logic.  ....    Tenth  edition,  corrected 
and  revised.    xv,i92  p.  S.     (Clarendon  Press  series.)     Oxford: 
Clarendon  Press,  i^9S.189f?«  (His  Logic  deductive  and 
inductive)  .  -  . 


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MONUFflCTURED  TO  fillM  STRNDRRDS 
BY  fiPPLIED  IMRGE,    INC. 


Class    I  O    h^  Book    I      0  'C 

Columbia  College  Library 

Madison  Av.  and  49th  St.  New  York. 
Beside  ihe  mam  topic  this  book  also  treats  of 


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DEDUCTIVE    LOGIC 


FOWLER 


a 


THE    ELEMENTS 


OF 


HENRY    FROWDE 


Oxford  University  Press  Warehousk 
Amen  Corner,  £.C. 


DEDUCTIVE    LOGIC 

DESIGNED    MAINLY  * 
FOR    THE    USE    OF  JUNIOR    STUDENTS 
IN    THE    UNIVERSITIES 


BY 


THOMAS    FOWLER,    D.D, 

President  of  Corpus  ChrisH  College 

Wykeham  Professor  of  I.o^ic  in  the  University  of  Oxford 

And  Honorary  Doctor  of  Laws  in  the  University  of  I-dinbur^rh 


NINTH    EDITION 
CORRECTED    AND    REVISED 

AT    THE    CLARENDON    PRESS 


MDCCCLXXXVII 


[  AH  rights  reserved'\ 


PREFACE. 


1 


THE  precise  object  of  the  following  pages  is  (without 
pre-supposing  any  technical  acquaintance  with  logical 
terminology)  to  enable  a  student  of  average  intelligence 
to  acquire  for  himself  an  elementary  knowledge  of  the 
main  problems,  principles,  and  rules  of  Deductive  Logic. 
They  are  not  designed  to  save  him  the  trouble  of  after- 
wards consulting  more  advanced  text-books,  either  in 
his  own  or  other  languages.  The  English  student  who 
wishes  to  gain  an  exact  and  detailed  knowledge  of  the 
relations  of  Deduction  to  Induction,  and  consequently 
of  the  true  place  and  value  of  the  former  process  in 
any  special  science,  must  still  have  recourse  to  the  works 
of  Mr.  Mill;  or,  if  he  wish  to  trace  the  history  of  logical 
terms  and  doctrines  (one  of  the  most  important  chapters 
in  the  history  of  both  ancient  and  modern  literature), 
he  must  still  consult  Sir  W.  Hamilton's  Lectures,  and  the 
Appendices  and  Notes  of  Dr.  Mansel  to  Aldrich's  Logic. 

To  these  works,  as  well  as  to  Archbishop  Whately's 
luminous  Chapter  on  Fallacies,  and  to  the  original  and 
suggestive  work  of  Mr.  James  Mill  on  the  Analysts  of 
the  Phenomena  of  the  Human  Mind,  the  Author  must, 
once  for  all,  express  his  obligations.  He  has,  however, 
endeavoured,  on  all  disputed  points,  to  reason  out  his 


98188 


VI 


PR  EFA  C E, 


own  conclusions,  feeling  assured  that  no  manual,  how- 
ever elementary,  can  be  of  real  service  to  the  student, 
unless  it  express  what  may  be  called  the  'reasoned 
opinions'  of  its  author. 

The  great  difficulty  to  be  encountered  by  any  writer 
of  an  English  Manual  of  Logic  is  the  *  unsetded  state 
of  our  logical  terminology.  Many  words  have  various 
significations,  or  are  used  in  different  senses  by  different 
writers,  and  often  there  are  no  recognised  terms  to 
express  some  distinction  which  it  is  still  incumbent  on 
the  logician  to  notice.  '  A  fixed  and  sufficient  terminology 
can,  however,  only  be  created  by  the  habit  of  teaching 
Logic,  and  of  carrying  on  our  discussions  on  the  science, 
in  our  own  language.  But  though,  in  some  respects, 
the  Latin  terminology  may  be  superior  to  our  own,  there 
can  be  no  question  that  the  language  in  which  men 
habitually  think  must  be  the  fittest  medium  for  analysing 
their  thoughts. 

The  Notes  appended  to  the  Chapters  (as  distinguished 
from  the  foot-notes)  are  designed  to  inform  the  student 
of  any  divergences  from  the  ordinary  mode  of  treatment, 
or  to  suggest  to  him  further  reading  on  topics  which, 
if  noticed  at  all,  are  only  alluded  to  in  the  text.  They 
may  be  omitted  on  the  first  reading. 

Besides  the  Notes  appended  to  the  various  Chapters, 
it  is  perhaps  desirable  that  the  student,  if  he  is  entirely 
unacquainted  with  logical  and  psychological  discussions, 
should  omit,  on  the  first  reading,  the  Chapters  on  the 
Relation  of  Logic  to  Psychology,  on  the  various  Kinds 


PR  EFA  CE, 


Vll 


of  Terms,  on  the  Denotation  and  Connotation  of  Terms, 
on  the  Relation  of  the  Predicate  to  the  Subject  of  a 
Proposition,  on  Verbal  and  Real  Propositions,  on  De- 
finitions, and  on  Divisions  and  Classifications.  Unfor- 
tunately, the  most  difficult  problems  which  the  logician 
has  to  solve  occur  at  the  outset  of  his  task. 

It  is  hoped  that,  independently  of  its  bearing  on 
University  studies,  a  Short  English  Manual  of  Logic  may 
be  used  with  advantage  in  the  Upper  Forms  of  Schools, 
and  that  it  may  not  be  without  interest  to  the  general 

reader. 

The  Manuals  of  Sanderson,  Wallis,  Aldrich,  «fec.,  owing 
to  the  peculiar  circumstances  of  the  period  in  .which  they 
were  written  (a  period,  which,  being  transitional,  retained 
not  only  much  of  the  scholastic  terminology,  but  also 
much  of  the  Realistic  doctrine),  have  ceased  to  be 
adapted  to  modern  instruction.  The  Author,  with  some 
misgivings,  and  a  keen  sense  of  the  difficulties  of  the 
task,  trusts  that  the  present  w^ork  may  be  found  use- 
fully to  occupy  their  place.  Its  propositions  cannot, 
however,  be  presented  in  the  same  curt  and  dogmatic 
shape,  for  we  have  learnt  to  regard  many  portions 
of  Logic,  like  many  portions  of  the  sciences  whose 
method  it  claims  to  analyse,  as  fairly  open  to  differences 
of  opinion. 


* .  *  In  the  Table  of  Contents  it  will  be  observed  that 
the  words  Definitions,  Divisions,  Classifications,  Infer- 
ences, Oppositions,  Conversions,  Permutations,  occur  in 


I 


VI 11 


PREFA  CE, 


place  of  the  more  ordinary  forms  Definition,  Division, 
Classification,  &c.  The  object  of  this  change  is  to 
suggest  to  the  student  the  importance  of  distinguishing 
the  results  from  the  processes  by  which  they  are  gained. 
Many  words  employed  in  Logic  and  Psychology  admit 
of  both  these  meanings,  and  it  is  only  by  prefixing  the 
indefinite  article  or  using  the  plural  number,  as  when 
we .  speak  of  '  a  definition '  or  '  definitions,'  that  we  can 
make  it  plain  that  we  mean  the  result  and  not  the 
process.  It  would  be  very  difficult  in  all  cases  to 
mark  the  distinction,  but  I.  have  endeavoured  to  do  so 
wherever  it  seemed  to  be  of  any  importance  ^ 

'  A  similar  confusion  in  many  of  the  terms  employed  in  Physics  has 
been  noticed  by  Mr.  [now  Sir  W.  R.]  Grove  {Correlation  of  Forces, 
fifth  ed.,  p.  251).  '  Another  confusion  of  terms  has  arisen,  and  has, 
indeed,  much  embarrassed  me  in  enunciating  the  propositions  put  forth 
in  these  pages  on  account  of  the  imperfection  of  scientific  language ; 
an  imperfection  in  great  measure  unavoidable,  it  is  true,  but  not 
the  less  embarrassing.  Thus,  the  words  light,  heat,  electricity,  and 
magnetism,  are  constantly  used  in  two  senses— viz.  that  of  the  force 
producing,  or  the  subjective  idea  of  force  or  power,  and  of  the  effect 
produced,  or  the  objective  phenomenon.  The  word  motion,  indeed, 
is  only  applied  to  the  effect,  and  not  to  the  force,  and  the  term 
chemical  affinity  is  generally  applied  to  the  force,  and  not  to  the 
effect ;  but  the  other  four  terms  are,  for  want  of  a  distinct  termin- 
ology, applied  indiscriminately  to  both.' 


PREFACE  TO  SUBSEQUENT  EDITIONS. 

IN  subsequent  Editions  several  minor  alterations  and 
additions  have  been  introduced  into  the  Text  of  some 
of  the  Chapters.  A  few  Notes,  as  well  as  an  Index  and 
a  Collection  of  Examples,  have  also  been  added.  In 
making  these  alterations  and  additions,  the  Author  has 
gladly  availed  himself  of  suggestions  kindly  offered,  from 
time  to  time,  by  various  correspondents  and  friends, 
amongst  whom  he  ought  specially  to  mention  Professor 
Park,  of  Belfast.  He  has,  however,  endeavoured  to  pre- 
vent the  work  from  materially  exceeding  the  limits  of  its 
original  size. 

Several  friends  have  suggested  to  the  Author  the  intro- 
duction of  two  new  chapters,  one  on  the  Categories,  the 
other  on  the  Formation  of  Terms.  Influenced  partly  by 
a  desire  not  to  increase  the  bulk  of  the  volume,  and  partly 
by  still  more  important  reasons,  he  has,  after  some  hesi- 
tation, decided  against  the  introduction  of  these  chapters. 
The  doctrine  of  Categories  is  important  in  the  history  of 
Logic  ^  but  it  is  not  properly  a  branch  of  Logic,  as  that 
word  is  now  generally  understood  and  as  it  has  been 
understood  throughout  this  work.  The  Formation  of 
Terms  is  a  subject  which  properly  belongs  to  Psychology 
and  not  to  Logic,  and  moreover  could  not  be  adequately 
treated  in  a  small  compass.  It  is  true  that  some  ques- 
-  tions  properly  belonging  to  Psychology  or  the  History  of 

^  On  the  categories  of  Aristotle  the  reader  is  referred  to  Hamilton's 
Lectures  on  Logic,  Lect.  xi.,  and  the  Appendix  to  Mansel's  Aldrich, 
Note  B.  Both  Sir  W.  Hamilton  and  Dr.  Mansel,  especially  the 
former,  insist  on  their  *  wholly  extra-logical '  character. 


PREFACE   TO  SUBSEQUENT  EDITIONS, 


Logic  have  been  noticed  in  various  parts  of  the  book, 
but  they  have  only  been  casually  alluded  to,  not  treated 
in  distinct  chapters.  Logic  has  always  been  over-weighted 
with  extraneous  matter,  and,  wherever  it  is  possible,  it  is 
desirable  to  relieve  it  of  its  superfluities,  though  much 
discretion  may  be  needed  in  the  process,  and  though  the 
requirements  of  examinations  have  a  constant  tendency 
to  lead  writers  on  Logic  to  consider  not  how  little,  but 
how  much  they  can  introduce  into  their  works. 

In  the  Fifth  and  subsequent  Editions,  the  Author  has 
added  an  Appendix  on  the  Heads  of  Predicables.  There 
is  no  branch  of  elementary  Logic  so  difficult  to  state  in  a 
form  at  once  satisfactory  to  the  teacher  and  intelligible  to 
the  learner.  The  attempt  at  a  scientific  treatment  which 
he  has  made  in  Pt.  IL  ch.  v.  is,  he  believes,  usually  found 
too  complicated  for  a  beginner.  As,  however,  he  cannot 
state  his  own  view  of  the  doctrine  in  a  simpler  form,  he 
has  thought  it  the  best  course  to  add  an  Appendix, 
which,  without  any  attempt  at  an  exhaustive  treatment, 
simply  offers  an  explanation  of  the  five  w^ords.  Genus, 
Species,  Differentia,  Property,  Accident.  This  Appendix, 
on  the  first  reading  of  the  book,  may  be  substituted  by  the 
student  for  Pt.  IL  ch.  v.,  but  should  be  combined  with 
the  formal  definitions  given  on  p.  45,  of  which,  in  fact,  it 
furnishes  an  explanation. 

The  principal  changes  in  the  eighth  Edition  are  the 
addition  of  notes  to  Pt.  III.  chs.  i.  and  vii.,  and  some 
alterations  in  the  text  of  the  latter  part  of  ch.  vii. ;  and, 
in  the  present  Edition,  certain  additions  to  the  latter  part 
of  ch.  vii.  and  to  the  foot-note  on  p.  73. 


)  I 


CONTENTS. 


Introduction. 


CHAP. 


I.  The  Relation  of  Logic  to  Psychology 
II.  Definition  of  Logic      .... 

III.  The  Relation  of  Thought  to  Language 

IV.  Division  of  the  Products  of  Thought 


PAGE 
1 


5 
7 
9 


PABT  I.     The  Term. 

I.  The  Various  Kinds  of  Terms      . 
II.  The  Denotation  and  Connotation  of  Terms 


II 

19 


PABT  II.     The  Proposition. 

I.  The  Subject  and  Predicate 23 

II.  The  Copula 25 

III.  Division  of  Propositions  according  to  their  Quantity 

and  Quality 28 

IV.  Distribution  of  Terms 33 

V.  Relation  of  the  Predicate  to  the  Subject  of  a  Proposition 

(Heads  of  Predicables}  .         .        .         .         .36 


Xll 


CONTENTS, 


CHAP. 


VI.  Verbal  and  Real  Propositions 

VII.  Definitions 

VIII.  Divisions  and  Classifications 


PART  III.     Inferences. 

I.  The  Various  Kinds  of  Inferences 

II.  Immediate  Inferences 

§  I.  Definition  of  an  immediate  Inference 

§  2.  Oppositions 

§  3.  Conversions 

§  4.  Permutations  .... 

III.  Mediate  Inference  or  Syllogism   . 

§  I.  Structure  of  the  Syllogism     . 

§  2.  Moods  and  Figures 

§  3.  Determination  of  the  Legitimate  Moods  of 
Syllogism,  including  the  Syllogistic  Rules, 
Reduction,  and  the  Special  Rules  of  the 
Figures 

,  IV.  Trains  of  Reasoning  (the  Sorites)        .        .        .        . 
V.  Complex  (Hypothetical)  Propositions  and  Syllogisms  . 
§  I.  Division  of  Complex  Proposirions  into  Con- 
junctive and  Disjunctive     .... 

§  2.  Conjunctive  Syllogisms 

§  3.  Disjunctive  Syllogisms 

§  4.  The  Dilemma 

VI.  On  the  words  '  Most,'  *  Many,'  &c.,  as  expressing  the 
Quantity  of  Propositions 


PAGE 
48 

49 
58 


68 

77 

77 

77 
So 

82 
84 

84 
88 


90 
109 
112 

112 
114 
116 
119 

124 


{ 


CONTENTS.  Xlii 

CHAP.  PAGE 

VIII.  Fallacies 140 

§  I.  Division  of  Fallacies 140 

§  2.  Fallacies  due  to  the  assumption  of  a  False 

Premiss 141 

'  §  3.  Fallacies  due  to  the  neglect  of  the  Laws  of 

Deductive  Inference 142 

§  4.  Fallacies  due  to  Irrelevancy          .         .         .  147 

§  5.  Fallacies  due  to  Ambiguity  of  Language     .  149 

IX.  On    Method,  as   applied  to   the  Arrangement  of  Syl- 
logisms in  a  Train  of  Reasoning     .         .         .         .156 

APPENDIX 160 

EXAMPLES 165 

INDEX ,        .  185 


■''-^<^^j^^^^n^^i^dt^'' 


VIL  Probable  Reasoning,  including  Circumstantial  Evidence     128 


ELEMENTS 


OF 


DEDUCTIVE    LOGIC 


'I 


r 


H 


INTRODUCTION. 


-M- 


CHAPTER  I. 


On  the  Relation  of  Logic  to  Psychology, 


% 


PSYCHOLOGY,  or  Mental  Philosophy,  may  be  defined 
as  the  science  which   classifies  and  analyses  the  pheno- 
mena of  the  human  mind.     It  notes  mental  phenomena, 
considers  them  in  their  mutual  relations,  and  investigates 
the  mode  of  their  generation.     Of  these  mental  pheno- 
mena some  are  called  emotional,  others  intellectual.     The 
intellectual  phenomena  may  be  regarded  as   the  result, 
partly  of  Perception,    partly  of  Imagination,  partly    of 
Comparison,  Reflexion,  or  Thought.     Perception  is  the 
act  or  operation  of  apprehending  some  present  pheno- 
menon.    Imagination  is  the  act  or  operation  of  repre- 
senting to  the  mind  some  absent  phenomenon.     Com- 
parison, Reflexion,  or  Thought,  is  the  act  or  operation 
of  comparing  phenomena,  whether  present  or  absent,  as 
well  as   of  comparing,  either  with   these   or  with   one 
another,    the  results    themselves  which   we   derive  from 
such  comparisons.     Thus  I  perceive  this  particular  rose 
before  me,  its  colour,  its  smell,  and  the  pleasure  I  derive 

W  1  B 


Ill 


II 


2  RELATION  OF  LOGIC 

from  seeing  and  smelling  it.  All  these  perceptions  I  can 
recall  to-morrow,  even  though  the  rose  be  absent,  by  the 
act  or  operation  of  imagination.  Lastly,  I  may  compare 
this  particular  rose  with  another  which  lies  on  the  table, 
or  with  one  which  I  saw  yesterday,  and  I  may  express 
their  similarity  by  calling  them  both  moss-roses,  or  their 
difference  by  calling  one  a  moss-rose  and  the  other  a 
Tudor  rose.  Again,  moss-rose  and  Tudor  rose,  which 
names  are  both  results  of  the  act  or  operation  of  com- 
parison, may  themselves  be  compared,  and  their  points 
of  similarity  expressed  by  the  word  '  rose.'  So  rose  and 
dahlia  may  be  compared,  and  their  points  of  similarity 
expressed  by  the  word  '  flower.'  Or  I  may  compare  the 
feeling  with  which  I  contemplate  the  rose  with  similar 
feelings  which  I  have  previously  experienced,  and  call 
it  'pleasure';  or  I  may  compare  it  with  the  feeling 
which  I  experience  when  I  prick  my  finger  with  a  thorn, 
and  call  one  ^pleasure,'  the  other  *pain';  or  I  may 
compare  pleasure  and  pain  themselves,  and  call  them 
both  'feelings.'  The  act  of  making  comparisons,  and 
of  apprehending  similarities  and  differences,  is  usually 
called  Thought  or  Thinking,  and  the  results  at  which  it 
arrives  Thought  or  Thoughts.  The  act  or  operation 
itself,  as  distinguished  from  other  mental  acts  or  opera- 
tions, and  the  results  which  ensue  from  its  correct  or 
incorrect  exercise,  are  alike  legitimate  subjects  of  inves-- 
ligation  for  the  psychologist  or  mental  philosopher. 
But  the  more  detailed  consideration  of  the  latter,  i.e. 
Thoughts  or  the  results  of  Thinking,  becomes  the  subject 


\ 


TO  PSYCHOLOGY,  3 

of  a  science  with  a  distinct  name,  Logic,  which  is  thus 
a  subordinate  branch  of  the  wider  science,  Psychology. 


Note  I. — The  term  Perception  is  here  used  in  its  or- 
dinary sense.  The  distinctions  between  External  and 
Internal  Perception,  Perception  Proper  and  Sensation 
Proper,  are  foreign  to  the  present  subject.  They  are 
discussed  at  great  length  in  the  works  of  Sir  William 
Hamilton  and  Dr.  Mansel,  as  well  as  in  those  of  the 
Scottish^'school  of  metaphysicians  generally,  but,  as  in- 
volving some  of  the  most  abstruse  and  disputed  questions 
in  Psychology,  it  is  not  necessary  or  desirable  that  the 
student  should  acquaint  himself  with  them  till  he  com- 
mences the  special  study  of  that  science. 

Note  2. — Imagination,  as  here  defined,  is  what  may  be 
called  Simple,  or  Reproductive,  as  distinguished  from 
what  may  be  called  Complex,  or  Productive  Imagination. 
The  former  simply  represents  to  the  mind  absent  objects 
of  perception  as  they  have  already  been  perceived,  the 
latter  combines  phenomena'/ or  portions  of  phenomena, 
whether  absent  or  present,  into  a  new  whole.  Thus  the 
notions  of  a  particular  man  or  a  particular  horse,  if  the 
man  and  horse  be  absent,  are  products  of  simple  or 
reproductive  imagination ;  the  notion  of  a  centaur  would 
be  a  product  of  complex  or  productive  imagination. 
For  further  and  more  precise  information  on  this  distinc- 
tion, which  is  here  necessarily  stated  somewhat  roughly, 

B  2 


RELATION  OF  LOGIC  TO  PSYCHOLOGY. 


see  Sir  W.  Hamilton's  Lectures  on  Metaphysics,  Lect.  xxxiii. 
The  creations  of  poetry  and  art  are  results  of  complex 
imagination,  or,  in  other  words,  of  repeated  processes  of 
simple  imagination  and  comparison.  Inasmuch  as  com- 
plex imagination  may  be  analysed  into  simple  imagina- 
tion and  comparison,  and  is  thus  not  one  of  the  ultimate 
acts  or  operations  to  which  our  mental  phenomena  are 
traceable,  it  would  have  been  beside  my  purpose  to  have 
noticed  it  in  the  text. 

Note  3. — I  have  employed  the  expression  'act  or 
operation/  avoiding  the  expression  'power  or  faculty/ 
as  the  latter  implies  a  theory  of  mental  phenomena  which 
would  be  rejected  by  many  psychologists.  It  has  been 
necessary  to  speak  of  'act  or  operation/  as  the  word 
'  act/  like  many  other  terms  of  logic  or  psychology,  may 
mean  either  the  operation  or  the  result.  This  is  an  in- 
stance at  the  very  outset  of  the  ambiguity  noticed  in  the 
paragraph  at  the  end  of  the  preface. 


« ^"^Gr^^^S^Si-^J-^ 


i' 


CHAPTER  II. 

Definition  of  Logic, 

IT  is  the  province  of  Logic  to  distinguish  correct  from 
incorrect  thoughts,  i*e.  to  analyse  those  thoughts  which 
are  accepted  by  mankind  as  indubitably  correct,  and  to 
point  out  wherein  they  differ  from  those  which  are  re- 
garded as  doubtful  or  incorrect ;  and,  as  a  consequence 
of  this  function,  it  is  also  its  province  to  lay  down  rules 
for  the  attainment  of  correct  thoughts  and  for  the  avoid- 
ance of  incorrect  thoughts.  Thus  Logic  is  both  a  Science 
and  an  Art.  It  is  a  Science,  inasmuch  as  it  furnishes  us 
with  a  knowledge  of  what  is,  inasmuch  as  it  is  an  analysis, 
and  determines  the  conditions  on  which  valid  thoughts 
depend.  It  is  an  Art,  inasmuch  as  it  lays  down  rules 
for  practice,  and  thus  enables  us  to  detect  incorrect 
thoughts  in  the  reasonings  of  others,  and  to  avoid  them 
in  our  own. 

Logic  may  therefore  be  defined  as  the  science  of 
the  conditions  on  which  correct  thoughts  depend,  and 
the  art  of  attaining  to  correct  and  avoiding  incorrect 
thoughts. 


Note. — This  definition  is  in  substance  that  given  by 
Mr.   Mill    in    his   Examination    of  Sir    W.   Hamilton's 


DEFINITION  OF  LOGIC, 


Philosophy,  p.  391  (third  ed.,  p.  448).  *  Logic/  he  says, 
*  is  the  art  of  thinking,  which  means  of  correct  thinking, 
and  the  science  of  the  conditions  of  correct  thinking/ 
The  word  *  thoughts'  is  substituted  for  *  thinking/  in 
order  to  bring  more  prominently  before  the  student,  what 
Mr.  Mill  himself  acknowledges,  the  fact  that  Logic  is 
concerned  with  the  products  or  results  rather  than  with 
the  process  of  thought,  i.  e.  with  thoughts  rather  than  with 
thinking,  though,  in  estimating  the  conditions  on  which 
correct  thoughts  depend,  it  is  necessary,  to  some  extent, 
to  take  account  of  the  processes  by  which  they  are 
formed.  It  seems  also  desirable  to  introduce  into  the 
definition  of  Logic  some  reference  to  *  incorrect  thoughts,' 
as  bringing  out  more  distinctly  the  character  of  Logic 
as  an  art,  and  asserting  for  it  the  right  of  investigating 
fallacies. 


CHAPTER  in. 
On  the  Relation  of  Thought  to  Language, 

WHETHER  it  is  possible  to  think  without  the  aid 
of  language,  is  a  question  which  has  been  a  constant 
source  of  dispute  amongst  logicians  and  psychologists. 
It  is  not  necessary,  however,  here  to  enter  on  this 
discussion.  As  all  logicians  are  agreed  that  we  cannot 
communicate  our  thoughts  without  the  aid  of  language, 
or  of  equivalent  signs,  and  that  practically  we  do  always 
think  by  means  of  language,  by  a  sort  of  internal  con- 
verse, it  will  be  safer  to  adopt  the  terminology  of  those 
authors  who  regard  our  thoughts  as  expressed  in  lan- 
guage rather  than  that  of  those  who  consider  or  attempt 
to  consider  them  in  themselves  as  apart  from  their  ex- 
pression in  words.  I  shall  therefore  speak  of  Terms  and  ' 
Propositions,  not  of  Concepts  and  Judgments. 


Note. — Sir  W.  Hamilton  and  his  followers,  regarding 
Logic  as  primarily  and  essentially  concerned  with  thought, 
and  only  secondarily  and  accidentally  with  language, 
attempt  to  mark  the  products  of  thought  by  words  which 
Ao  not  imply  their  expression  in  language.     Thus,  instead 


8        RELATION  OF  THOUGHT  TO  LANGUAGE. 

of  Terms  and  Propositions,  they  use  respectively  the 
words  Concepts  and  Judgments.  The  word  Syllo- 
gism, owing  to  the  ambiguity  of  the  Greek  word  X^oy, 
stands  either  for  the  internal  thought  or  the  external 
expression  of  it.  (See  Hamilton's  Lectures  on  Logic, 
Lecture  i.) 


«i-^^N»S)S>''3v^ 


w 


CHAPTER  IV. 

Division  of  the  Products  of  Thought, 

IT  has  been  stated  that  thought  is  the  act  or  operation 
of  comparison.  Its  simplest  result  is  that  which  is  ex- 
pressed by  the  Term.  Terms  may  be  combined  into 
Propositions,  and  Propositions,  either  singly  or  in  con- 
junction with  one  or  more  other  propositions,  may  lead 
to  Inferences.  I  shall  treat  in  order  of  the  Term, 
of  the  Proposition,  of  Inferences.  Before  proceeding 
further,  it  may  perhaps  be  useful  to  the  student  to  give 
by  anticipation  instances  of  these  products  or  results 
of  thought.  Man,  good,  manliness,  goodness,  the  good- 
ness of  man,  the  virtue  of  manliness,  are  all  instances 
of  terms.  '  This  man  is  good,'  '  All  citizens  of  a  state 
are  under  an  obligation  to  obey  its  laws,'  are  instances 
of  Propositions,  and,  according  to  logical  phraseology, 
*  good  '  is  said  to  be  predicated  of  '  this  man,'  and  '  under 
an  obligation  to  obey  its  laws '  is  said  to  be  predicated 
of  '  all  citizens  of  a  state.*  The  term  predicated  is  called 
the  Predicate-^  and  the  term  of  which  it  is  predicated  is 
called  the  Subject^  the  word  *  is '  or  *  are '  (or,  in  the  case 
of  negative  propositions,  'is  not'  or  *are  not'),  which 
connects  the  two,  being  called  the  Copula.  Lastly,  we 
may  take  as  instances  of  Inferences  the  following: — 


} 


lO  DIVISION  OF  THE  PRODUCTS  OF  THOUGHT, 

'  No  rectilineal  figure  is  contained  by  less  than  three 
lines ; 

Therefore,  no  figure  contained  by  less  than  three  lines 
is  a  rectilineal  figure. 

All  Englishmen  are  of  mixed  descent, 
This  is  an  Englishman ; 
Therefore,  he  is  of  mixed  descent. 

The  last  proposition  (which  is  called  the  conclusion) 
is  said  to  be  inferred  from  the  proposition  or  pro- 
positions which  precede  it  (called  X\it  premiss  ox  pre- 
misses). 


*^~--^^<5*>5fe^^>^i.'-» 


M 


PART   I.— The  Term. 


CHAPTER  I. 
On  the   Various  Kinds  of  Terms. 

A  TERM  (so  called  from  terminus,  a  boundary,  be- 
cause the  terms  are  the  two  extremes  or  boundaries  of 
the  proposition)  is  a  word  or  combination  of  words 
which  may  stand  by  itself  as  the  subject  or  predicate  of 
a  Proposition ;  it  expresses  either  an  individual,  a  group 
of  individuals,  an  attribute,  or  a  group  of  attributes.  This 
definition  obviously  excludes  all  articles,  adverbs,  inter- 
jections, conjunctions,  prepositions,  and  oblique  cases  of 
nouns.  It  also  excludes  verbs;  for  though  a  verb  ex- 
presses attributes,  and  often  serves  at  once  for  the  copula 
and  the  predicate  (or  part  of  the  predicate),  as  in  the  pro- 
positions '  John  walks,'  '  William  fears  Thomas,'  it  must, 
in  a  logical  proposition  stated  according  to  strict  form, 
always  be  analysed  into  the  copula  and  participle :  thus 
the  above  propositions,  when  stated  logically,  become 
*John   is  walking/   'William   is  fearing   Tliomas  ^'     A 

^  A  proposition  of  which  the  verb  is  not  analysed  into  the  copula 
and  a  participle  is  called  by  the  older  logicians  '  sectmdl  adjacentis^ 
in  contradistinction  to  the  form  of  proposition  as  ordinarily  stated  in 
Logic,  which  is  called  *  tertii  adjacejitis'  Thus  vir  currit  is  a  pro- 
position secimdi  adjacentis,  vir  est  currens  is  a  proposition  tertii 
adjacentis. 


12 


VARIOUS  KINDS  OF  TERMS. 


VARIOUS  KINDS  OF  TERMS. 


13 


pronoun  is  only  significant  as  standing  in  the  place  of  a 
substantive,  and  therefore  we  may  limit  ourselves  to  the 
consideration  of  substantives,  adjectives,  and  participles. 

By  the  older  logicians  a  terra  was  defined  as  a  Cale- 
gorematic  word  (from  KaT,,y6pr,iia  '  something  which  can  be 
predicated'),  i.e.  a  word  or  combination  of  words  which 
can  stand  by  itself  as  the  predicate  of  a  proposition.  All 
words  or  combinations  of  words  which  require  to  be 
joined  with  some  other  word  or  words  in  order  to  serve 
this  purpose  were  called  Syncategorematic  words. 

It  has  been  said  that  a  term  expresses  an  individual, 
a  group  of  individuals,  an  attribute,  or  a  group  of  attri- 
butes.   If  it  expresses  an  individual,   as   Socrates,  the 
present  Queen  of  England,  the  sea,  hie,  ille,  hoc,  iUud 
&c.,  It  IS  called  a  (i)  Singular  Term.    If  it  expresses  a 
group  of  individuals,  it  may  either  be  applicable  to  each 
mdividual  of  the  group  severally  as  well  as  to  the  group 
collectively,  or  to  the  group  coUectively  but  not  to  each 
mdividual  severally.     Thus  the  terms,  man,  horse,  flower, 
are  not  only  applicable  to  each  individual  of  the  groups 
which  they  express,  but  also  to  the  groups  collectively; 
I  can  say,  'John  is  a  man,' '  Thomas  is  a  man,' '  this  is 
a  horse,"  that  is  a  horse,'   'the  rose  is  a  flpwer,'  'the 
dahlia  is  a  flower,'  &c.    But  I  cannot  say  '  Caius  is  the 
fourteenth    legion,'    'Pompey    is    the    Roman    senate,' 
though    I    can    predicate   'fourteenth    legion'    or  'the 
Roman  senate '  of  the  groups,  taken  collectively,  which 
these  terms  express.    In  the  former  case  the  term  is 
called  a  (2)  Common  Term,  in  the  latter  a  (3)  Colleclive 


r 


Term,  A  collective  term  may  by  a  slight  change  of 
phraseology  be   expressed   as   a    common   term;    thus, 

*  Roman   senate'  may    become    'Roman    Senators/   or 

*  fourteenth  legion  *  '  soldiers  of  the  fourteenth  legion.' 
But,  as  it  stands,  a  collective  term  is,  in  predication,  as 
will  be  noticed  hereafter,  equivalent  to  a  singular  term. 

A  common  term  is  equally  applicable  to  each  indi- 
vidual severally  of  the  group  which  it  expresses,  and  it  is 
so  in  virtue  of  certain  points  of  similarity  which  all  the 
individuals  possess  in  common.  It  is  in  fact  because  we 
have  observed  that  they  all  possess  certain  attributes  in 
common,  that  we  are  able  to  call  them  by  a  common 
name.  Thus  a  common  term,  like  man,  horse,  &c.,  at 
once  suggests  to  me  a  certain  group  of  individuals  and 
a  certain  group  of  attributes  which  is  predicable  of  each 
of  these  individuals  severally.  But  there  are  other  terms, 
called  (4)  Attributives,  and  (5)  Abstract  Terms,  which  ex- 
press attributes  or  groups  of  attributes  only.  Attribu- 
tives may  be  distinguished  from  Abstract  Terms  by  the 
fact  that  they  may  form  the  predicate,  but  cannot,  unless 
joined  with  a  singular,  collective,  common,  or  abstract 
term,  form  the  subject  of  a  proposition.  Grammatically, 
they  are  represented  by  adjectives  and  participles,  when 
not  used  substantively.  Of  this  class  are  the  terms, 
human,  red,  heavy,  brave,  willing,  thinking,  running,  &c., 
when  not  used  substantively.  Thus  I  may  say,  '  Socrates 
is  human/  but,  when  I  wish  to  employ  the  term  '  human ' 
in  the  subject  of  a  proposition,  I  must  append  to  it  some 
such  word  as   *  being,'   and   say  *  this  human  being  is 


14 


VARIOUS  KINDS  OF  TERMS, 


VARIOUS  KINDS  OF  TERMS, 


15 


I 


i- 


SocratesV  Such  terms  have,  in  fact,  no  signification, 
unless  used  substantively,  or  in  conjunction  with  a  sub- 
stantive, either  as  qualifying  it  or  as  predicated  of  it. 

Abstract  Terms,  on  the  other  hand,  not  only  express 
mere  attributes  or  groups  of  attributes,  but  may  be 
thought  of  without  any  reference  to  the  individuals  of 
which  these  attributes  are  predicable.  Of  this  class  are 
such  terms  as  humanity,  colour,  figure,  fortitude,  &c.  To 
it  may  be  referred  sentences  employing  the  indicative 
mood  and  introduced  by  the  word  '  that,'  infinitive  moods, 
some  instances  of  adjectives  and  participles  used  substan- 
tively, and  generally  every  term,  being  neither  singular, 
collective,  nor  common,  which  may  be  employed  both  as 
the  subject  and  as  the  predicate  of  a  proposition. 

All  the  terms  discussed  above  may  be  employed  as 
predicates  of  propositions.  Attributives  alone  cannot  be 
employed  as  subjects. 

We  have  thus  divided  terms  into  singular,  collective, 
and  common  terms,  attributives,  and  abstract  terms.  It 
must  however  be  borne  in  mind  that  many  of  those  attri- 
butives and  abstract  terms  which  are  most  frequently  in 
use,  or  which  have  been  for  a  long  time  in  use,  have 
come  to  be  employed  as  common  terms.  Thus  we  some- 
times speak  of  red,  good,  virtue,  figure,  number,  pleasure, 

^  It  is  perhaps  hardly  necessary  to  remark  that  in  such  phrases  as 
'  Great  is  Diana  of  the  Ephesians,'  '  Great  is  my  rejoicmg,'  the  places 
of  the  subject  and  predicate  are  reversed,  for  the  sake  of  laying 
greater  emphasis  on  the  predicate.  In  a  logical  analysis  of  such 
propositions,  the  subject  and  predicate  must  be  restored  to  their 
normal  positions. 


colour,  &c.  (both  in  the  singular  and  plural  number), 
exactly  as  if  they  were  common  terms,  though  they  still 
retain  in  other  connexions  their  use  as  abstract  terms 
or  attributives.  This  remark  will  be  found  of  great 
importance  in  some  of  the  subsequent  sections. 


Note  I. — Nothing  has  been  said  above  of  the  com- 
mon distinction  between  abstract  and  concrete  terms. 
An  abstract  term  would  be  defined  as  a  term  expressive 
of  an  attribute  or  group  of  attributes  considered  apart 
from  the  individuals  of  which  it  is  predicable;  a  con- 
crete term  as  a  term  expressive  of  an  attribute  or  group 
of  attributes  considered  in  reference  to  the  individuals 
of  which  it  is  predicable,  as  well  as  of  an  individual  or 
group  of  individuals  itself  The  terms  John,  the  tenth 
legion,  man,  human,  would  all  be  called  concrete; 
humanity  would  be  called  an  abstract  term^.  It  will 
be  noticed  that  I  have  availed  myself  of  the  expression 
*  abstract  term,'  but  avoided,  as  too  wide  to  be  of  prac- 
tical service,  the  contrasted  expression  'concrete  term.' 
Concrete  terms  include  what  I  have  called  attributives, 
as  well  as  singular,  collective,  and  common  terms. 

^  Mr.  Mill  {Logicj  bk.  i.  ch.  ii.  §  4)  states  that  Locke  and  several 
later  writers  have  applied  the  expression  *  abstract  name'  to  all 
general  names,  that  is,  attributives  and  common  terms  as  well  as 
what  I  have  called  abstract  terms.  This  statement,  however,  is  not 
uniformly  true  of  Locke.  See,  for  instance,  Essay,  bk.  iii.  ch.  viii. 
Mr.  Mill  himself,  following  the  practice  of  the  Schoolmen,  takes  the 
expression  in  the  same  limited  sense  as  in  the  text.  By  the  older 
logicians  singular  and  collective  terms  were  not  regarded  as  concrete, 
110  account  being  taken  of  them  in  this  distinction. 


"I 


i6 


VARIOUS  KINDS  OF  TERMS. 


VARIOUS  KINDS  OF  TERMS. 


17 


Note  2.— The  term   'attributive'   (which  has  already 
been  employed  by  Harris  and  James  Mill)  is  used  in 
preference  to  the  term  'adjective/  both  because  it  in- 
cludes participles,  and  because  it  seems  undesirable  in  a 
work  on  Logic  to  employ  a  technical  term  of  Grammar. 
Harris  (Hermes,  bk.  i.  ch.  vi.)  includes  amongst  '  attribu- 
tives '  verbs;  but  a  verb,  as  has  already  been  stated,  is,  in 
Logic,  always  represented  by  the  copula  and  a  participle. 
I  have  placed  attributives  before  abstract  terms,  be- 
cause they  are  more  nearly  allied  to  singular,  collective, 
and  common  terms,  being,  for  the  most  part,  either  pre- 
dicated of  these  terms  or  employed  to  qualify  them. 
They  seem  also  as  a  rule  to  precede  abstract  terms  in 
their  formation.    Thus  human,  red,  brave,  good,  willing, 
must  have  been  employed  before  the  corresponding  terms 
humanity,  redness,  bravery,  goodness,  willingness. 

Note  3.— For  the  sake  of  completeness,  I  have 
spoken  of  a  term  as  expressing  an  attribute  or  a  group 
of  attributes.  There  is  however  no  distinct  name  for  a 
term  expressing  a  single  attribute  incapable  of  analysis, 
and  the  only  peculiarity  of  such  terms  is,  as  will  be 
seen  below,  that  they  are  incapable  of  definition.  Locke 
called  attributes  which  were  incapable  of  analysis  '  simple 
ideas,'  but  the  expression  '  simple  term '  would  not  be 
applicable  in  a  corresponding  sense. 

Note  4.— That  common  terms,  attributives,  and  ab- 
stract terms  are  formed  from  a  comparison  of  individual 
objects  or  groups  of  objects,  and  that  consequently  they 
are  results  of  thought,  is  obvious.    But  it  may  not  be  so 


r 


easy  to  perceive  that  this  is  the  case  with  singular  and 
collective  terms.  These  terms  however  are  appropriated 
to  individual  objects  or  groups  of  objects  in  order  to 
distinguish  them  from  others,  and  the  necessity  for  such 
distinction  can  only  arise  after  a  comparison  of  this  or 
that  individual  or  group  with  others,  and  a  perception 
of  certain  points  of  resemblance  and  difference  between 
them.  Unless  I  had  observed  some  difference  between 
John  and  Thomas,  this  table  and  that,  the  thirteenth 
legion  and  the  fourteenth,  it  would  never  have  occurred 
to  me  to  distinguish  them  by  separate  names ;  but  this 
very  observation  of  a  difference  involves  an  act  of  com- 
parison, and  consequently  an  act  of  thought. 

Note  5. — It  is  important  to  notice  that  in  a  series  of 
terms,  like  man,  human,  humanity,  all  expressing  the 
same  attributes,  the  later  and  more  abstract  terms  can 
hardly  fail  to  suggest  the  earlier  and  more  concrete, 
and  it  is  so  because  the  earlier  terms  of  the  series  have 
been  longer  formed  and  are  therefore,  as  a  rule,  more 
familiar  to  us.  Thus  'humanity'  can  hardly  fail  to 
suggest  to  us  the  word  '  human,'  from  which  it  is  formed, 
and  *  human '  will  suggest  the  word  *  man,'  from  the  Latin 
equivalent  of  which  it  is  also  formed,  and  whose  attributes 
it  expresses.  Nor  can  we  use  the  word  'man'  without 
thinking  of  this  or  that  individual  man  with  whom  we  are 
familiar.  A  common  term,  in  fact,  expresses  simply  an 
individual  object  divested  of  all  its  peculiar  attributes,  and 
regarded  as  possessing  only  those  attributes  which  it  has 
in  common  with  all  the  other  objects  which  are  desig- 

c 


i8 


VARIOUS  KINDS  OF  TERMS. 


nated  by  the  same  name.  But  it  is  indifferent  on  which 
object  of  the  group  the  mind  concentrates  its  attention, 
and  we  are  all  along  conscious  that  the  particular  object 
selected  is  simply  representative  of  the  group.  And  hence 
it  is  that  a  common  name  simultaneously  suggests  to 
the  mind  a  group  of  individual  objects  and  a  bundle 
of  attributes  characteristic  of  that  group.  For  a  further 
discussion  of  this  subject,  see  Hamilton's  Lectures  on 
Metaphysics,  Lect.  xxxv.  and  xxxvi. ;  Hansel's  Prolego- 
mena Logi'ca^  ch.  i. ;  and  Mill's  Examination  of  Hamilton, 
ch.  xvii. 

Note  6. — Mr.  Mill  maintains  that  attributives,  when 
employed  as  predicates,  are  really  common  terms.  Thus 
the  propositions  '  All  triangles  are  three-sided,'  '  All  wise 
men  are  just,'  are  regarded  by  him  as  only  abbreviated 
modes  of  saying  'All  triangles  are  three-sided  figures,' 
'All  wise  men  are  just  men.'  I  should  allow  that  the 
attributive  in  the  predicate,  when  taken  in  conjunction 
with  the  subject,  always  suggests  a  common  term  which 
may  be  substituted  for  it,  as  in  the  syllogism  *A11  wise 
men  are  virtuous,  All  virtuous  men  are  happy ; .-.  All  wise 
men  are  happy/  But,  though  the  attributive  may  always 
admit  of  being  expressed  as  a  common  term,  while  it 
continues  to  be  expressed  as  an  attributive  there  seem  to 
be  present  to  the  mind  only  attributes,  whereas,  when  it 
becomes  a  common  term,  there  seems  also  to  be  present 
a  group  of  individuals  possessing  those  attributes. 


CHAPTER  H. 

On  the  Denotation  and  Connotation  of 

Terms, 

A  TERM  may  be  said  to  denote  or  designate  individuals 
or  groups  of  individuals,  to  connote  or  mean  attributes  or 
groups  of  attributes  ^ 

^  It  ought,  perhaps,  to  have  been  stated  in  the  earlier  editions  of 
this  work  that  the  term  connotation  is  here  employed  in  a  some- 
what different  sense  from  that  which  is  attached  to  it  either  in  the 
scholastic  logic  or  in  the  system  of  Mr.  Mill. 

In  the  scholastic  logic,  a  cofttiotative  term  is  '  one  which  primarily 
signifies  an  attribute,  secondarily  a  subject,'  as  *  white,'  the  contrasted 
term  being  called  an  *  absolute  term,'  as  '  man '  or  *  whiteness.'  See 
Mansel's  Aldrich,  cap.  i,  §  3,  note  g. 

According  to  Mr.  Mill's  nomenclature,  a  connotative  term  is  one 
which  *  denotes  a  subject  and  implies  an  attribute.' 

By  Mr.  Mill,  not  only  singular  and  collective,  but  also  abstract 
terms  are  regarded  as  non-connotative.  In  the  scholastic  logic, 
what  I  have  called  attributives  are  alone  recognised  as  connotative 
terms.     See  Mill's  Logic,  Bk.  I.  ch.  ii.  §  5. 

As  the  term  is  already  employed  with  so  much  uncertainty,  it 
appears  to  me  not  inexcusable  to  claim  still  further  licence,  and  to 
appropriate  the  expressions  '  denotation '  and  '  connotation '  of 
'  terms '  in  a  sense  parallel  to  that  which  is  expressed  by  the  dis- 
tinction between  the  '  extension '  and  the  '  intension  '  of  a  *  notion  ' 
or  'concept,'  applying  'denotation'  simply  to  the  objects,  and 
*  connotation  '  simply  to  the  attributes  which  are  signified  by  a  term. 
This  is  a  broad  and  exceedingly  convenient  distinction,  and,  notwith- 
standing the  apparent  paradox  involved  in  it,  namely,  that  '  abstract 
terms  are  not  denotative,'  I  believe  that  the  general  employment  of 
the  expressions  in  this  sense  would  considerably  simplify  the  state- 
ment and  explanation  of  many  logical  difficulties. 

C  2 


20 


DENOTATION  AND 


CONNOTATION  OF  TERMS, 


21 


In  the  first  place,  a  term  may  serve  to  denote  or 
point  out  an  individual  object  or  group  of  individuals. 
Thus  '  Socrates '  denotes  or  points  out  and  distinguishes 
from  all  others  the  individual  man  Socrates.  The  ex- 
pression '  tenth  legion  *  denotes  or  points  out,  and  dis- 
tinguishes from  all  other  collections  of  men,  the  particular 
group  known  as  the  tenth  legion.  Similarly,  the  word 
'  man '  denotes  or  points  out,  and  distinguishes  from  all 
other  groups,  a  certain  group  of  individuals  to  each 
member  of  which  and  to  each  member  of  which  only 
the  word  '  man '  may  legitimately  be  applied.  All  terms 
of  this  kind,  therefore,  viz.  singular,  collective,  and 
common  terms,  are  denotative;  but  terms  like  human, 
white,  humanity,  whiteness,  i.e.  attributes  and  abstract 
terms,  are  not  denotative,  except  mediately,  that  is,  so 
far  as  they  suggest  the  common  terms  'human  beings,' 
*  white  things.' 

In  the  second  place,  a  term  may  serve  to  connote 
attributes  or  groups  of  attributes.  Thus  terms  like 
humanity,  human,  man,  viz.  abstract,  attributive,  and 
comtnon  terms,  are  all  connotative,  that  is,  they  at 
once  suggest  or  imply  attributes.  But  singular  and 
collective  terms  like  *  Socrates,*  *the  tenth  legion,'  are 
not  connotative,  except  so  far  as  they  suggest  common 
terms.  This  remark  requires  some  explanation.  A  col- 
lective term  like  ^the  tenth  legion,'  'the  House  of 
Commons,'  at  once  suggests  the  corresponding  common 
term,  'soldiers  of  the  tenth  legion,'  or  'members  of 
the  House  of  Commons ' ;  and  this  common  term  may 


\ 


connote  any  number  of  attributes,  but,  as  the '  attributes 
are  suggested  mediately  through  the  common  term  and 
not  directly  by  the  collective  term,  the  collective  term  is, 
strictly  speaking,  non-connotative.  The  same  is  the  case 
with  a  singular  term.  A  term  like  '  William '  may  sug- 
gest to  me  '  man,'  '  male,'  *  Englishman,'  '  one  of  my 
friends,'  &c.,  and  so  may  become  connotative,  but  it  is 
in  itself  rightly  regarded  as  non-connotative,  inasmuch 
as  it  suggests  to  me  these  attributes  only  through  the 
medium  of  the  common  terms  to  which  it  is  referred. 

It  appears  therefore  that  common  terms  are  both 
denotative  and  connotative;  that  singular  and  collective 
terms  are  denotative,  but  not  connotative ;  that  abstract 
terms  and  attributives  are  connotative,  but  not  denota- 
tive ;  and  finally,  that  mediately,  as  suggesting  common 
terms,  any  non-connotative  term  may  become  connotative 
and  any  non-denotative  term  denotative. 


Note. — The  distinction  between  the  denotation  and 
connotation  of  a  term  is  often  otherwise  expressed,  as  that 
between  the  extension  and  intension  (or  comprehension)^  or 
the  extensive  and  intensive  (or  comprehensive)  capacity, 
or  the  breadth  and  depth,  of  a  notion.  Having  adopted 
the  phraseology  which  designates  the  simplest  product  of 
thought  as  a  term,  instead  of  a  notion,  I  shall  speak 
of  the  extensive  and  intensive  (or  comprehensive)  ca- 
pacity of  a  term.  The  extensive  capacity  of  a  term 
is   measured   by  the    number    of  individuals  which    it 


22     DENOTATION  AND   CONNOTATION  OF  TERMS, 

designates    (denotes),   the    intensive    or    comprehensive 
capacity  of  a  term  by  the  number  of  attributes  which  it 
includes,  suggests  or  implies  (connotes).     It  is  plain  that 
in  a  series  of  common  terms,  standing  to  one  another  in 
a  relation  of  subordination,  the  denotation  and  connota- 
tion, or  the  extensive  and  intensive  capacities,  of  the  term 
are  so  related,  that  as  the  one  increases  the  other  de- 
creases, and  vice  versa.    Thus,  if  we  arrange  in  order  any 
series  of  common  terms,  as  flower,  rose,  moss-rose,  we 
see  that  'flower,'  which  implies  the  smallest  number  of 
attributes,  is  applicable  to  the  largest  number  of  indi- 
viduals ;  *  moss-rose,'  which  is  applicable  to  the  smallest 
number   of  individuals,   implies   the   largest   number   of 
attributes :  and  generally  in  any  series  of  common  terms 
arranged  in  subordination,  the  larger  the  denotation  or 
extensive   capacity,  the   smaller    is    the   connotation   or 
intensive  capacity,  and  vice  versa.     In  conformity  with 
this   principle,   the  singular   term  which    stands  for  the 
individual,  and  is  smallest  in  denotation,  is,  when  we  refer 
it  to  the  various  common  terms  which  may  be  predicated 
of  it,  and  so  assign  to  it  mediately  an  intensive  capacity, 
the  largest  in  connotation.    Thus  the  term  Socrates,  when 
I  regard  it  as  expressing  one  who  was  a  philosopher,  a 
teacher,  a  martyr,  a  soldier,  an  Athenian  citizen,  &c.,  &c., 
suggests  to  me  far  more  attributes  than  any  one  of  these 
common  terms  singly. 


. 


PART  II. — The  Proposition. 

CHAPTER  I. 
On  the  Subject  and  Predicate, 

A  PROPOSITION  asserts  or  denies,  as  the  result  of 
comparison,  some  word  or  combination  of  words  of  some 
other  word  or  combination  of  words,  as  e.  g.  '  James  is 
the  man  I  saw  yesterday';  'No  rectilineal  figure  is 
contained  by  less  than  three  lines '  ;  *  Some  stars  are 
not  planets.'  As  before  stated,  the  words  or  combina- 
tions of  words  thus  employed  are  called  terms,  the 
term  affirmed  or  denied  is  called  the  predicate,  the  term 
of  which  it  is  affirmed  or  denied  the  subject,  the  con- 
necting verb,  whether  qualified  or  not  by  the  negative 
particle,  the  copula,  and  the  predicate  is  said  to  be 
predicated  of  the  subject.  In  the  above  examples,  '  the 
man  I  saw  yesterday,'  'contained  by  less  than  three 
straight  lines,'  and  '  planets '  are  predicates  and  are  /r^- 
^//r^/^d/ respectively  of 'James,'  'all  rectilineal  figures,'  and 
'  some  stars,'  as  subjects.  In  the  first  case  the  predicate  is 
predicated  affirmatively,  a  fact  which  is  expressed  by  the 
copula  '  is ' ;   in  the  two  last  negatively,  a  fact  which  is 


24 


THE  SUBJECT  AND  PREDICATE, 


expressed  by  the  copula  Ms  not.'  These  remarks  may 
appear  inconsistent  with  the  form  of  the  second  example, 
but  '  no  rectilineal  figure  is,  &c/  is  really  an  abbreviated 
and  unambiguous  mode  of  stating  the  longer  and  am- 
biguous proposition  '  All  rectilineal  figures  are  not,  &c.' 

The  word  *  predicated,'  as  equivalent  to  'asserted  or 
denied,'  is  here  used  in  a  wider  than  its  ordinary  signifi- 
cation. In  common  language,  we  say  such  and  such 
an  attribute  cannot  be  predicated  of  such  and  such  a 
term,  using  'predicated'  as  equivalent  to  'asserted'  and 
as  opposed  to  '  denied.'  All  ambiguity  may  be  avoided 
by  speaking  of  the  predicate  as  predicated  affirmatively 
or  predicated  negatively  of  the  subject. 


^ 


t 


CHAPTER  II. 
On  the  Copula. 

THE  Logical  Copula,  it  being  its  office  simply  to  serve 
as  a  sign  of  predication,  is  limited  to  the  present  tense  of 
the  verb  '  to  be,'  with  or  without  the  addition  of  the  nega- 
tive particle,  according  as  the  proposition  is  negative  or 
affirmative.  This  limitation  follows  from  the  fact  that  it  is 
simply  the  office  of  the  proposition  to  express  my  present 
judgment  as  to  the  compatibiUty  or  incompatibility  of  two 
terms.  Hence  all  reference  to  time,  past  or  future,  and 
even  to  time  present,  as  respects  the  terms  themselves, 
and  not  my  judgment  as  to  their  compatibility,  must  be 
expressed  in  the  predicate  and  not  in  the  copula.  I  may, 
for  brevity's  sake,  say  '  fire  burns,'  '  Alexander  was  the  son 
of  Philip,'  '  The  guns  will  be  fired  to-morrow,'  and,  in  con- 
versation or  discussion,  it  would  undoubtedly  be  pedantic 
to  express  the  propositions  otherwise;  but  formally,  for 
the  purpose  of  being  estimated  logically,  I  must  resolve 
them  into  their  logical  elements,  and  say  '  Fire  is  burning,' 
'  Alexander  is  a  person  who  was  son  of  Philip,'  'The  firing 
of  the  guns  is  an  event  which  will  take  place  to-morrow.' 

Not  only  does  the  logical  copula  convey  no  notion  of 
time  with  reference  to  the  terms  themselves  (or,  to  speak 
more  accurately,  the  things  signified  by  them),  but  it  is 
also  divested  of  the  notion  of  existence.     In  other  words, 


26 


THE   COPULA, 


it  is  employed  simply  as  a  connecting  particle,  not  as  a 
substantive  verb.  Where  the  substantive  verb  is  used  in  a 
logical  proposition,  it  must  be  expressed  in  the  predicate. 
Thus  'I  am/  'The  king  is  not,'  become  'I  am  existent,' 
'  The  king  is  non-existent.'  That  the  copula  implies  no 
notion  of  existence  is  evident  from  the  fact  that  we  can 
use  such  propositions  as  these  :  '  The  labours  of  Hercules 
are  a  myth/  '  He  is  a  nonentity.' 

Can  we  modify  the  copula  so  as  to  express  certainty, 
probability,  possibility,  or  other  modes  of  connexion  be- 
tween the  subject  and  the  predicate?  This  is  the  cele- 
brated question  of  Modality,  a  question  which  has  been 
the  source  of  much  difference  of  opinion  amongst  logi- 
cians. Even  though  it  were  granted  that  the  proposition 
simply  expresses  our  present  judgment  on  the  compati- 
bility or  incompatibility  of  two  terms,  it  might  be  main- 
tained that  it  should  express  the  nature  of  our  judgment 
and  the  degree  of  our  assent  or  dissent,  whether  it  be 
certain,  approximating  to  certainty,  or  faltering.  Thus  it 
might  be  maintained  that  the  following  should  be  accepted 
as  instances  of  the  ultimate  analysis  of  a  logical  proposi- 
tion :  *  This  is  certainly  the  man  I  saw  yesterday,'  '  This 
is  probably  the  man  I  saw  yesterday,'  *  This  is  possibly 
the  man  I  saw  yesterday.'  That  we  use  these  forms  in 
conversation  and  discussion  is  unquestionable,  but  it  is 
one  main  object  of  Logic  to  analyse  our  abbreviated  infer- 
ences and  statements  into  their  full  logical  equivalents.  In- 
stead therefore  of  admitting  various  descriptions  of  copulse 
(other  than  the  affirmative  and  negative),  in  order  to  adapt 


( 


THE   COPULA. 


27 


Logic  to  ordinary  language,  it  seems  simpler,  as  well  as 
more  scientific,  to  insist  on  the  uniform  character  of  the 
copula,  and  to  represent  propositions  like  the  foregoing 
as  predicating  our  degree  of  assent  to  or  dissent  from 
the  sentence  in  question.  Thus,  after  asking  myself  the 
question  '  Is  this  the  man  I  saw  yesterday  ? '  I  may  either 
answer  simply  '  Thi^  is  the  man  I  saw  yesterday,'  or  I  may 
describe  the  degree  of  my  assent  by  stating  '  That  this  is 
the  man  I  saw  yesterday  is  certain,  probable,  possible,'  &c. 
In  fact,  such  propositions  seem  to  be  the  result  of  an  act 
of  reflexion  on  the  degree  of  our  own  conviction. 

I  shall  therefore  regard  the  form  A  is  or  is  not  B  as  the 
ultimate  and  uniform  logical  analysis  of  all  propositions, 
though  I  shall  occasionally,  for  the  sake  of  brevity,  avail 
myself  of  the  forms  sanctioned  by  popular  language. 


]S!oie.—k.%  regards  the  expression  of  time  in  the  copula, 
the  student  will  find  the  opposite  opinion  to  that  taken  in 
the  text  adopted  by  Mr.  Mill,  Logic,  vol.  i.  ch.  iv.  §  2.  In 
support  of  my  view,  he  may  refer  to  Dr.  Mansel's  Prole- 
gomena Logica,  pp.  63,  64.  On  the  question  of  expressing 
in  the  copula  the  degrees  of  assurance  with  which  a  pro- 
position is  entertained  ('certainly/  'probably/  &c.),  see 
Sir  W.  Hamilton's  Discussions,  pp.  i45-7»  and,  for  a  more 
qualified  view  than  that  taken  either  by  Sir  W.  Hamilton 
or  myself.  Dr.  Mansel's  Prolegomena  Logica,  note  G. 


f 


DIVISION  OF  PROPOSITIONS. 


2Q 


CHAPTER  III. 

Division  of  Propositions  according  to  their 
Quantity  and  Quality, 

WE  have  already  seen  that  propositions  are  either 
affirmative  or  negative,  according  as  the  copula  used  is 
of  the  form  *  is '  or  'is  not/  This  is  called  a  division  of 
propositions  according  to  their  Quatity, 

They  are  further  divided,  according  to  their  Quantity^ 
into  Universal  and  Particular.  For,  in  affirming  or 
denying  a  predicate  of  a  subject,  it  is  obvious  that  I 
may  either  affirm  or  deny  the  predicate  of  all  the  indi- 
viduals denoted  by  the  subject,  or  of  part  only.  Thus 
in  affirming  mortality  of  man,  I  may  say  *  All  men  are 
mortal,'  or  '  Some  men  are  mortal ' ;  in  denying  wisdom 
of  man,  I  may  deny  it  of  all  men  or  only  of  some 
men,  i.  e.  I  may  say  '  No  men  are  wise,'  or  '  Some 
men  are  not  wise/  When  the  predicate  is  affirmed  or 
denied  of  all  the  individuals  denoted  by  the  subject,  the 
proposition  is  called  an  Universal  Proposition;  when 
of  part  only,  a  Particular  Proposition.  A  Singular  Pro- 
position, i.e.  a  proposition  of  which  the  subject  is  a 
singular  term,  ranks  as  an  Universal,  because  the  pre- 
dicate is  affirmed  or  denied  of  everything  (i.  e.  in  this 


case,  the  one  thing)  denoted  by  the  subject.  The  same 
remark  holds  good  of  a  proposition  in  which  the  subject 
is  a  collective  term.  An  attributive,  as  we  have  already 
seen,  cannot,  by  itself,  be  used  as  the  subject  of  a  pro- 
position. Abstract  terms  which  have  come  to  be  used  as 
common  terms,  and  admit  of  plurals,  as  figure,  triangle, 
virtue,  pleasure,  &c.,  have  a  denotative  power,  and 
may,  like  common  terms,  form  the  subjects  of  either 
universal  or  particular  propositions.  But  those  abstract 
terms,  like  humanity,  wisdom,  &c.,  which  retain  their 
orio-inal  characteristic  of  being  connotative  only,  and 
admit  of  no  plurals,  simply  express  an  attribute  or  group 
of  attributes  with  which,  as  a  whole,  it  is  asserted  or 
denied  that  the  predicate  is  compatible;  consequently, 
a  proposition,  of  which  such  a  term  is  the  subject, 
ranks  as  an  universal. 

Thus  such  propositions  as  ^Ambition  is  aggressive,' 
'Wisdom  is  a  virtue,'  'The  fourteenth  legion  is  dis- 
banded,' '  Socrates  is  an  Athenian  citizen,'  are,  on  the 
very  face  of  them,  universals.  But  propositions  in  which 
the  subject  is  a  common  term  or  an  abstract  term  used 
as  a  common  term,  must  be  quantified ;  that  is,  we  must 
attach  to  the  subject  either  an  universal  or  a  particular 
designation.  It  is  not  sufficient  to  say,  'triangles  are 
figures/  'horses  are  black';  we  must  state  whether  we 
mean  that '  all  triangles '  or  '  some  triangles '  are  '  figures/ 
whether  we  mean  that  '  all  horses '  or  '  some  horses '  are 
black.  '  Indefinite '  or  '  indesignate '  propositions,  as  they 
are  called,  i.e.  propositions  in  which  the  subject,  being 


'<\\ 


30 


DIVISION  OF  PROPOSITIONS, 


QUANTITY  AND   QUALITY. 


31 


a  common  term,  is  not  quantified,  are   inadmissible .  in 

Logic. 

By  combining  the  division  of  propositions  into  uni- 
versal and  particular  with  that  into  affirmative  and  nega- 
tive we  obtain  four  forms,  viz. — 

Universal  Affirmative.  All  X  is  Y.  (A) 

Universal  Negative.  No  X  is  Y.  (E) 

Particular  Affirmative.  Some  X  is  Y.  (I) 

Particular  Negative.  Some  X  is  not  Y.  (O) 

I  shall  in  future  designate  these  forms  of  proposition 
respectively  as  A,  E,  I,  0\     • 


Note. — Sir  W.  Hamilton^,  followed  by  several  other 
logicians,  maintains  that  in  thought  the  predicate  is 
always  quantified  as  well  as  the  subject.  He  proposes 
to  reform  the  logical  theory  of  the  proposition  accord- 

^  It  sometimes  requires  a  little  ingenuity  to  state  a  given  proposi- 
tion in  one  of  the  above  forms.  Thus  the  propositions  *  None  but 
the  brave  deserve  the  fair,'  *  The  wise  alone  are  good,'  *  Not  every 
historian  is  worthy  of  credit,'  '  All  his  acts  are  not  defensible,'  when 
stated  in  strictly  logical  form,  become  respectively.  No  not-brave  (or 
None  who  are  not  brave)  are  deserving  of  the  fair.  No  not-wise  (or 
None  who  are  not  wise)  are  good,  Some  historians  are  not  worthy 
of  credit.  Some  of  his  acts  are  7iot  defensible.  The  simplest  equi- 
valents of  the  two  former  propositions  are.  All  who  deserve  the 
fair  are  brave.  All  good  men  are  wise ;  but  these  are  arrived  at  by 
permutation  and  conversion,  two  forms  of  inference  which  have 
not  yet  been  explained. 

Sir  William  Hamilton's  theory  was  anticipated  in  a  work  now 
little  read,  but  full  of  original  suggestions  on  logical  questions,  Mr. 
George  Bentham's  Outline  of  a  New  System  of  Logic,  published  in 
1827. 


ingly,  and  in  lieu    of  the  four  ordinary  forms  of  pro- 
position substitutes  the  following  :— 

All  X  is  all  Y. 
All  X  is  some  Y. 
All  X  is  not  any  Y. 
All  X  is  not  some  Y. 

Some  X  is  all  Y. 
Some  X  is  some  Y. 
Some  X  is  not  any  Y. 
Some  X  is  not  some  Y. 

This  scheme,  if  adopted,  would,  as  Sir  W.  Hamilton 
shews,  reduce  all  conversion  to  simple  conversion,  render 
nugatory  any  discussion  as  to  the  distribution  of  terms, 
and  considerably  simplify  the  forms  of  syllogism:  see 
the  Appendices  to  Sir  W.  Hamilton's  Discussions,  and 
to  his  Lectures  on  Logic.  Amongst  other  criticisms  may 
be  seen  Mr.  Mill's  in  his  Examination  of  Hamilton  s 
Philosophy,  ch.  xxii.  It  wx)uld  of  course  be  undesirable 
to  enter  here  into  any  discussion  as  to  the  merits  of 
Sir  W.  Hamilton's  theory,  but,  as  reasons  for  not  adopt- 
ing the  quantification  of  the  predicate  in  the  present 
work,  it  may  be  sufficient  to  state  (i)  that,  as  to  utility, 
the  trouble  entailed  by  quantifying  the  predicate  in  every 
proposition  would  probably  far  exceed  that  saved  by 
simplifying  the  forms  of  Conversion  and  Syllogism ;  (2) 
that  the  forms  of  expression  given  above  are  not  merely 
unusual,  but  are  such  as  we  never  do  use ;  whereas, 
though  the  analysis  of  our  thoughts  frequently  leads  to 


32 


DIVISION  OF  PROPOSITIONS. 


forms  of  expression  which  are  unusual,  this  would,  if 
admitted,  be  the  only  case  in  which  it  led  to  forms 
which  are  never  used  at  all ;  (3)  that  some  of  the  above 
propositions  really  contain  in  a  compressed  form  two 
ordinary  propositions,  as  e.  g.  '  All  A  is  all  B,'  contains 
the  two  ordinary  propositions  'AH  A  is  B'  and  'All 
B  is  A,'  the  proposition  'Some  A  is  all  B'  contains  the 
two  ordinary  propositions  '  Some  A  is  B '  and  '  All  B  is  A,' 
whereas  it  is  the  object  of  Logic  not  to  state  our  thoughts 
in  a  condensed  form  but  to  analyse  them  into  their 
simplest  elements. 


i»-«:iF^5ci^ii-<r 


CHAPTER  IV. 
Distribution  of  Terms. 

A  TERM  is  said  to  be  distributed,  when  it  is  employed 
in  its  entire  extent,  i.  e.  when  it  applies  to  all  the  indivi- 
duals denoted  by  the  name.  Thus,  when  we  say,  *all 
men,'  'no  men,'  *man'  is  distributed;  when  we  say  'some 
men,'  it  is  undistributed.  This  phraseology  of  course 
applies  directly  only  to  common  terms ;  but  singular  and 
collective  terms,  as  has  already  been  explained,  are  always 
taken  in  an  universal  acceptation,  or,  in  other  words,  are 
always  distributed.  The  same  is  true  of  those  abstract 
terms  which  have  not  come  to  be  used  as  common  terms, 
because  they,  as  it  were,  personify  the  attribute  or  group 
of  attributes  which  they  express ;  so  far  as  regards  dis- 
tribution, they  are,  in  fact,  virtually  singular  terms.  In 
such  propositions  as,  *  This  is  wisdom,'  '  Wisdom  is  jus- 
tified of  her  children,'  '  Warmth  is  essential  to  growth,' 
'Knowledge  is  power,'  it  is  obvious  that  the  abstract 
terms  are  distributed  precisely  as  if  they  were  singular 
terms,  and  that,  for  all  logical  purposes,  these  proposi- 
tions rank  as  universal.  Attributives,  i.e.  adjectives  and 
participles,  have  no  meaning  except  in  connexion  with  a 
substantive.  They  must  either  be  prefixed  to  a  substantive 
or  predicated  of  it :  we  cannot  say  '  human '  alone ;  we 
must  either  speak  of  '  human  being,'  '  humai)  nature,'  &c., 


34 


DISTRIBUTION  OF  TERMS. 


DISTRIBUTION  OF  TERMS. 


35 


or  say,  '  So  and  so  is  human/  Consequently  the  distri- 
bution or  non-distribution  of  an  attributive,  as  *  human/ 
*red,'  &c.,  follows  that  of  the  corresponding  common 
term,  *  human  being,'  '  red  thing/  &c. 

Hence  we  perceive  that  a  singular,  collective,  or  abstract 
term  is  distributed  wherever  it  may  occur  in  a  proposition. 
We  have  therefore  only  to  enquire  as  to  the  distribution 
of  common  terms  and  attributives.  With  regard  to  these, 
the  two  following  rules  may  be  laid  down. 

1.  All  "universal  propositions  distribute  their  subject, 
whereas  particular  propositions  do  not.  This  rule  is 
obvious.  The  very  word  'air  or  'no'  shews  that  the 
subject  is  distributed,  whereas  the  word  'some'  shews 
that  it  is  undistributed. 

2.  All  negative  propositions  distribute  their  predicate, 
whereas  affirmative  propositions  do  not.  For  in  every 
negative  proposition  we  necessarily  exclude  from  the 
subject  every  individual  denoted  by  the  predicate,  but  in 
an  affirmative  proposition  we  do  not  necessarily  include 
in  the  subject  every  individual  denoted  by  the  predicate. 
Thus,  if  I  say,  '  No  crows  are  yellow,'  *  Some  cherries 
are  not  red,'  I  exclude  from  the  group  'crows'  every 
individual  object  denoted  by  the  term  '  yellow  things,'  and 
from  the  group  'some  cherries'  every  individual  object 
denoted  by  the  term  'red  things ^'     But  if  I  say,  'All 

»  Here  it  will  be  noticed  that  the  terms  *  yellow '  and  '  red,'  though  ^ 
not  in  themselves  denotative,  suggest  the  corresponding  common 
terms, '  yellow  things '  and '  red  things,'  and  thus,  through  the  medium 
of  the  common  terms,  become  denotative. 


men  are  animals,'  or  '  Some  Englishmen  are  poe^s,'  I  do 
not  include  in  the  group  'men'  all  animals,  nor  in  the 
group  '  Englishmen '  all  poets.  It  may  of  course  happen 
that  the  predicate  in  an  A  or  I  proposition  is  co-exten- 
sive with  the  subject,  as  in  the  propositions  'All  men 
are  rational  animals/  '  Some  men  are  poets/  but  this  fact 
is  accidental,  and  is  not  implied  in  the  form  of  the  pro- 
position. 

From  these  two  rules  we  infer  that,  in  the  case  of 
common  terms  and  attributives,  an  A  proposition  dis- 
tributes its  subject  only,  E  both  its  subject  and  pre- 
dicate, I  neither,  O  its  predicate  only.  If  a  term  be 
singular,  collective,  or  abstract,  it  is  invariably  dis- 
tributed. 


D  2 


CHAPTER  V. 

Relation  of  the  Predicate  to  the  Subject  of  a 
Proposition  {Heads  of  Predicables) 

N.B.  For  this   Chapter,  in  the  case  of  heginnersy  may  be 
substituted  Appendix,  p,  1 60.     See  Preface,  p.  x. 

FROM  what  has  already  been  said,  it  is  plain  that  a 
singular,  collective,  or  abstract  term,  inasmuch  as  it  is 
always  distributed,  cannot  form  the  subject  of  an  I  or 

0  proposition :  on  a  little  reflexion  it  will  also  be  plain 
that  the  predicate  of  a  proposition  cannot  be  singular, 
collective,  or  abstract,  unless   the  subject  be  the  same. 

1  have  already  noticed  that  an  attributive  can  never 
form  the  subject  of  any  proposition.  These  considera- 
tions will  be  found  to  simplify  the  problem  before  us. 

This  problem  may  be  stated  thus :  How  may  the  pre- 
dicates of  propositions  be  classified  in  relation  to  their 
subjects  ?  or  What  are  the  heads  of  predicables  (pr^di- 
cabilia,  things  or  words  that  may  be  predicated)?  I 
shall  discuss  the  four  forms  of  proposition  in  order. 

To  commence  with  A,  and  with  the  special  case  where 
both  subject  and  predicate  are  common  terms,  or  abstract 


RELATION  OF   THE  PREDICATE,  ETC.        37 

terms  which  are  used  as  common  terms  ^.     Here  'the  pre- 
dicate may  either  be  (i)  equivalent  in  extent  to  the  sub- 
ject, or  (2)  greater ;  it  cannot  be  less.     We  can  say,  for 
instance, '  All  men  are  animals,'  or  *  All  men  are  rational 
animals,'  but  we  cannot  say  'AH  animals  are  men.'    Now, 
if  the  predicate  be  (i)  equivalent  in  extent  to  the  subject, 
it  is  either  (a)  a  Synonym,  as  *  A  wold  is  a  down ' ;  or 
(p)  a  Definition,  as  *  A  plane  triangle  is  a  three-sided  recti- 
lineal figure ' ;   or  (y)  a  combination  of  a  genus  (a  term 
which  will  be  explained  immediately)  with  some  attribute 
which   is   peculiar   to   the   term  in   question  (called  by 
Aristotle  an  Xhiov  or  *  peculiarity '),  as  *  A  plane  triangle  is 
a  rectilineal  figure  the  sum  of  whose  angles  is  equal  to 
two  right  angles.'     A  synonym,  it  need  hardly  be  stated, 
is  an  equivalent  word,  and  a  definition  is  an  exposition 
of  the  connotation  of  a  term.     Now  it  will  be  observed 
that  the  definition  of  a  plane  triangle  consists  of  two  parts, 
one  in  which  it  is  designated  as  a  '  rectilineal  figure ' — 
a  wider   group,  which   includes   not   only  triangles  but 
other  rectilineal  figures— and  the  other  part  an  attribu- 

^  It  may  perhaps  assist  the  student  in  following  what,  to  be  exhaus- 
tive, must  necessarily  be  a  tedious  disquisition,  if  I  afford  him  some 
clue  to  the  order  in  which  the  cases  will  be  discussed  : — 

In  the  A  proposition,  (i)  if  the  predicate  be  a  common  term,  the 
subject  may  be  (a)  a  common,  (j8)  a  singular  or  collective  term  ; 
(2)  if  the  predicate  be  a  singular  or  collective  term,  the  subject 
must  be  the  same ;  (3)  if  the  predicate  be  an  abstract  term,  the 
subject  must  be  the  same ;  and  (4)  if  the  predicate  be  an 
attributive,  the  subject  may  be  (a)  a  common,  (jS)  a  singular  or 
collective,  (7)  an  abstract  term.  The  discussion  of  the  cases  in 
I,  E,  and  O  is  much  less  elaborate. 


Ui 


38 


RELATION  OF  THE  PREDICATE 


I 


tive,  *  three-sided/  which  distinguishes  triangles  from  all 
other  groups   contained   in   the  wider   group   to   which 
triangle   has   been   referred.      The   former    part   of  the 
definition  is  called  the  genus,  and  with  reference  to  it 
'plane  triangles,'  the  group  of  figures  defined,  are  called 
a  specks ;   the  latter  part  of  the  definition,  '  three-sided,' 
which   distinguishes   triangles   from   squares,  pentagons, 
and  other  rectilineal  figures  which  are  designated  by  the 
wider  term,  is  called  the  differentia  or  '  differencing '  attri- 
bute.    It  is  obvious  that  there  might  be  more  than  one 
of  these,  and  then  they  would  be  called  the  differenticB. 
With  reference  to  the  third  case,  *A  plane  triangle  is 
a  rectilineal  figure  the  sum  of  whose  angles  is  equal  to 
two  right  angles,'  *  rectilineal  figure '  is,  as  before,  to  be 
regarded  as  a  genus,  but  the  attributive  *  having  the  sum 
of  its  angles  equal  to  two  right  angles*  cannot  be  regarded 
as  a  differentia,  for  it  is  not  connoted  by  the  term  *  plane 
triangle,'  but  requires  to  be  proved  of  it;  at  the  same  time 
it  is  an  attribute  peculiar  to  the  plane  triangle,  and  hence, 
retaining  the  Aristotelian  term,  we  may  call  it  an  l^iov. 
Lastly,  there  remains  (2)  the  case  in  which  the  predicate 
is  of  greater  extent  than  the  subject,  both  being  com- 
mon terms,  as  in  the  propositions  *  All  men  are  animals,' 
'All  triangles  are  figures/     Here  the  subject  denotes  a 
smaller  group  of  individuals  included  under  the  wider 
group  designated  by  the   predicate;    that   is,  according 
to  the  nomenclature  already  explained,  the  predicate  is 
related  to  the  subject  as  genus  to  species.     This  relation  is 
often  spoken  of  as  that  of  the  containing  to  the  contained. 


TO   THE  SUBJECT  OF  A  PROPOSITION,        39 

When  the  predicate  is  a  common  term,  and  the  sub- 
ject a  singular  or  collective  term,  as  in  the  instances 
'Socrates  is  a  philosopher,'  *  Socrates  is  an  Athenian 
citizen,'  'The  House  of  Commons  is  a  branch  of  the 
legislature,'  the  predicate  is  related  to  the  subject  as  a 
group  of  individuals  to  an  individual,  i.  e.  as  a  species  to 
an  individual,  for  the  word  'genus'  is  only  applicable  to 
a  group  containing  other  groups.  The  same  account 
must  be  given  of  those  propositions  in  which  the  pre- 
dicate is  an  abstract  term  employed  as  a  common  term, 
and  the  subject  is  an  abstract  term  employed  strictly  as 
such,  as  e.  g.  '  Temperance  is  a  virtue,'  '  Heat  is  a  mode 

of  motion.' 

When  the  predicate  is  a  singular  or  collective  term, 
the  subject  must,  as  we  have  already  seen,  be  a  similar 
term.  Moreover  the  predicate  in  these  propositions  is 
always  distributed  as  well  as  the  subject,  and  conse- 
quently the  two  terms  are  co-extensive.  But,  inasmuch 
as  singular  and  collective  terms  have,  at  least  directly,  no 
connotation,  the  predicate  cannot  stand  to  the  subject  in 
the  relation  of  a  definition,  or  of  an  Xhiov"^  (i.e.  an  attribute 
peculiar  to  the  subject)  combined  with  a  genus.  It  can 
only  be  (i)  a  synonym,  or  (2)  a  singular  or  collective 
term  designating  the  individual  or  the  collective  group.  As 
instances  of  these  propositions  we  may  take  the  following: 
*  Cephas  is  Peter,'  '  Socrates  is  the  son  of  Sophroniscus,' 
« This  is  the  man  whom  I  saw  yesterday,  and  whom  I  told 

a  The  English  word  'characteristic'  might  perhaps  be  employed 
as  the  equivalent  of  the  Greek  lliov. 


.Hi 


40 


RELATION  OF  THE  PREDICATE 


TO   THE  SUBJECT  OF  A  PROPOSITION,        4I 


to  come  to  me/  *  The  fourteenth  legion  is  the  legion  quar- 
tered in  Britain.'  When  the  predicate  is  not  a  synonym, 
it  may  perhaps  be  called  a  Designation. 

When  the  predicate  is  an  abstract  term,  the  subject 
must  be  abstract  as  well,  and,  as  in  the  case  of  singular 
and  collective  terms,  the  subject  and  predicate  are  both 
distributed,  and  consequently  are  of  equal  extent.  We 
may  take  as  instances  of  the  various  forms  vv^hich  propo- 
sitions of  this  kind  assume,  *  Charity  is  love,'  '  Honesty  is 
the  best  policy,'  *  Definition  is  the  exposition  of  the  con- 
notation of  a  term.'  Now  in  the  first  example  '  love '  is 
intended  as  a  synonym  of  *  charity,'  in  the  second  'the  best 
policy'  is  predicated  of  '  honesty'  as  distinguishing  it  from 
all  other  courses  of  conduct;  the  third  example  is  an  ordi- 
nary case  of  a  definition.  The  case  of  two  abstract  terms 
may  therefore  be  regarded  as  identical,  so  far  as  concerns 
the  relation  of  the  predicate  to  the  subject,  with  that  of 
two  common  terms  which  are  co-extensive. 

Lastly,  there  remains  the  case  in  which  the  predicate  is 
an  attributive.  Supposing  the  subject  to  be  a  common  term, 
the  predicate  may,  as  we  have  seen,  be  (i)  a  differentia,  as 
in  the  proposition  '  All  triangles  are  three-sided,'  or  (2)  an 
taioi/,  as  in  the  proposition  '  All  plane  triangles  have  the 
sum  of  their  angles  equal  to  two  right  angles.'  Or,  though 
neither  a  differentia  nor  an  tStov,  it  may  be  (3)  what,  along 
with  the  XhiQv,  modern  logicians  would  call  a  Property,  viz. 
an  attribute  which,  though  not  connoted  by  the  subject, 
nor  even  peculiar  to  it,  follows  from  something  connoted 
by  the  subject,  either  (a)  as  effect  from  cause  or  (/3)  as 


conclusion  from  premiss  ^  An  instance  of  (a)  a  property 
which  follows  from  the  connotation  of  the  subject  hy  demon- 
stration would  be  given  in  the  proposition  *  A  parallelo- 
gram has  its  opposite  sides  equal,'  or  in  the  proposition 

*  A  circle  is  a  figure  the  ratio  of  whose  circumference  to  its 
diameter  is  approximately  3.14159  :  i.'  As  instances  of 
propositions  in  which  the  predicate  expresses  (3)  a  pro- 
perty following  from  the  connotation  of  the  subject  by 
causation,  we  may  take  '  Men  are  capable  of  combining  for 
purposes  of  joint  action,'  '  Water  communicates  pressure 
equally  in  all  directions.'  The  first  property  follows  from 
rationality,  or  that  combined  with  the  power  of  articulate 
speech,  which  seems  to  be  connoted  by  the  very  word 

*  man ' ;  the  second  property  follows  from  the  fluidity  of 
water.  The  last  example  of  a  property  following  by  way 
of  demonstration  and  the  first  of  a  property  following  by 
way  of  causation  are  Xhia  in  the  sense  of  Aristotle,  as  well 
as  propria  in  the  sense  of  the  later  logicians.  There  is 
(4)  one  other  case,  that  in  which  the  attributive,  though 
neither  connoted  by  the  subject  nor  following  from  any- 
thing connoted  by  the  subject,  is  predicable  of  everything 
denoted  by  it.  Such  an  attributive  is  called  an  Inseparable 
Accident,  and  the  common  instance  given  by  logicians  is 
the  proposition  '  All  crows  are  black.'     If  the  blackness  of 

crows  could  be  connected  by  way  of  causation  with  any 

• 
'  The  student  must  bear  in  mind  that  every  lliov  is  a  Property, 
though  every  Property  is  not  an  Xliov,     The  definition  given  above 
applies  only  to  those  properties  which  are  not  t3to.     The  formal 
definition  of  Property  will  be  found  on  p.  45. 


42 


RELATION  OF  THE  PREDICATE 


attribute  connoted  by  the  name,  it  would  be  regarded  as  a 
property;  if,  on  the  other  hand,  a  crow  could  be  found 
which  was  not  black,  blackness  would  be  degraded  to 
the  rank  of  a  Separable  Accident,  a  term  which  will  be 
explained  below. 

We  have  thus  far  considered  attributives  as  predicates 
in  the  special  case  where  the  subject  is  a  common  term. 
Where  the  subject  is  a  singular  or  collective  term,  and 
consequently  has  no  direct  connotation,  the  attributive 
forming  the  predicate  can  only  be  an  inseparable  accident  *. 
I  may  indeed  say  *  Socrates  is  rational,'  but  I  predicate 
rationality  of  him  as  man,  not  as  Socrates.  Where  the 
subject  is  an  abstract  term,  the  attributive  which  forms  the 
predicate  may  be  a  differentia  or  a  property,  but  cannot 
be  an  inseparable  accident,  for  an  abstract  term  denotes 
no  individuals. 

In  the  I  proposition  we  are  not  concerned  with  singular, 
collective,  or  abstract  terms.  If  the  predicate  be  (i)  a  com- 
mon term,  it  may  be  related  to  the  common  term  in  the 

*  Sometimes  a  distinction  is  drawn  between  the  separable  and  in- 
separable accidents  of  an  individual.  An  inseparable  accident  of  an 
individual  is  regarded  as  one  which  is  predicable  of  it  at  all  times, 
a  separable  accident  as  predicable  only  at  certain  times.  Thus  in  the 
propositions,  '  John  is  tall,'  'John  is  sitting  down,"  tall '  is  regarded 
as  an  inseparable,  'sitting  down'  as  a  separable  accident.  But  the 
expressions  separable  and  inseparable  accident  are  here  employed  in 
an  entirely  different  sense  from  that  in  which  they  have  been  employed 
above,  and  it  seems  preferable  to  regard  all  attributes  which  are 
predicated  of  individuals,  in  their  individual  character,  as  inseparable 
accidents— inseparable,  that  is  to  say,  from  the  mdividual  under  the 
circumstances  in  which  it  is  at  present  placed. 


TO    THE  SUBJECT  OF  A  PROPOSITION,        43 


subject  either  (a)  as  species  to  genus,  or  (^)  as  species  to 
species,  as  e.  g.  '  Some  men  are  poets,'  or  '  Some  poets  are 
philosophers.'  The  latter  relation  is  that  of  two  groups, 
which  have  some  members  in  common — overlapping 
species,  as  they  have  been  called.  The  relation  may  also 
be  (y)  that  oi genus  to  species,  as  '  Some  men  are  animals,' 
*Some  poets  are  men,'  but  this  form  of  proposition  is 
practically  useless,  as  it  stops  at  a  particular  assertion 
when  an  universal  assertion  is  legitimate.  If  the  predi- 
cate be  (2)  an  attributive,  it  must,  unless  the  proposition 
state  less  than  the  truth,  be  a  Separable  Accident,  i.e. 
an  attribute  which  is  true  only  of  some  of  the  individuals 
denoted  by  the  subject,  as  e.  g.  *  Some  men  are  black,' 
'  Some  triangles  are  equilateral.'   . 

With  regard  to  negative  propositions,  it  is  not  necessary 
to  speak  at  any  length.  The  negation  of  an  attributive 
in  an  E  proposition  implies  that  it  is  neither  a  differentia, 
property,  nor  accident;  in  an  O  proposition  that  it  is 
neither  a  differentia,  property,  nor  inseparable  accident, 
though  it  may  be  a  separable  accident.  All  that  has  been 
said  of  the  relations  of  singular,  collective,  and  abstract 
terms,  as  subjects,  either  to  similar  terms  or  to  common 
terms  and  attributives,  as  predicates,  in  the  case  of  an  A 
proposition,  holds  good  also,  mutatis  mutandis,  of  similar 
relations  in  E.  It  may  perhaps  be  as  well  to  give  a  few 
instances  of  such  propositions  :  '  Socrates  is  not  a  poet,' 
*  Socrates  is  not  the  man  I  saw  yesterday,'  'The  fourteenth 
legion  is  not  engaged  in  the  battle,'  '  Charity  is  not  obtru- 


%. 


% 


44 


RELATION  OF  THE  PREDICATE 


II 


sive/  *  Ambition  is  not  a  virtue/  Where  a  common  term 
is  denied  of  a  singular  or  collective  term,  it  stands  to  the 
subject  in  the  relation  of  species  to  individual.  Where 
a  common  term  is  denied  of  a  common  term,  there  is 
nothing  to  prevent  the  terms  being  extremely  remote  from 
each  other  and  hardly  admitting  of  comparison ;  but  here 
the  most  appropriate  relation  is — in  an  E  proposition, 
that  of  co-ordinate  though  exclusive  species,  i.e.  of  species 
which  having  many  characteristics  in  common,  and  both 
falling  immediately  under  the  same  genus,  still  denote  no 
individuals  in  common, — in  an  O  proposition,  that  of 
overlapping  species.  Thus  we  should  be  far  more  likely 
to  derive  information  from  such  propositions  as  these, 

*  No  sandstone  is  limestone,'  *  Some  astronomers  are  not 
mathematicians,'  than  from  such  propositions  as  these, 

*  No  men  are  trees/  '  Some  stones  are  not  vipers.' 

From  what  has  been  said  we  have  derived  the  follow- 
ing names  for  the  predicate  in  its  relation  to  the  subject : 
(i)  syyionym,  (2)  definition,  (3)  designation,  {4) genus,  {^)  spe- 
cies, (6)  diferentia,  (7)  Xh^ov,  {^) property  (not  being anXhiov), 
(9)  inseparable  accident,  (10)  separable  accident.  Of  these, 
logicians  have  neglected  synonym  and  designation,  the 
former  probably  on  account  of  its  slight  importance,  the 
latter  perhaps  because  it  applies  only  to  singular  and  col- 
lective terms.  Definition  is  analysed  into  genus  and  dif- 
ferentia ;  no  distinction  is  drawn  by  later  logicians  between 
i8ta  and  those  properties  which  are  not  peculiar  to  the  sub- 
ject, both  being  alike  designated  by  the  word  '  property' ; 


f  CJ 


TO    THE  SUBJECT  OF  A  PROPOSITION,        45 

and  the  word  *  accident '  serves  alike  for  separable  and 
inseparable  accident.     Genus,  difference,  species,  property, 
and  accident,  are  known  as  the  five  heads  of  predicables. 
These  may  be  briefly  defined  as  follows  : — 

A  Genus  is  a  common  term  expressive  of  a  wider 
group  of  individuals  including  narrower  groups. 

A  Species,  in  reference  to  a  genus,  is  a  common  term 
expressive  of  a  narrower  group  included  in  the 
genus;  in  reference  to  an  individual,  of  a  group 
including  it. 

A  Differentia  is  an  attributive  which  expresses  part 
of  the  connotation  of  some  common  term,  and 
which  distinguishes  that  term  from  all  other  species 
which  fall  under  the  same  genus. 

A  Property  is  an  attributive  which  does  not  express 
any  part  of  the  connotation  of  the  common  term, 
but  which  follows  from  some  part  of  the  connota- 
tion of  the  term,  either  as  an  effect  from  a  cause, 
or  as  a  conclusion  from  premisses. 

An  Accident  is  an  attributive  which  may  be  predicated 
of  the  whole  or  part  of  the  individuals  denoted 
by  a  common  term,  or  which  may  be  predicated 
of  an  individual,  but  which  is  neither  connoted 
by  the  common  term  nor  to  be  inferred  from 
anything  which  is  connoted  thereby  ^. 

5  In  the  above  definitions,  wherever  the  expression  *  common  term  ' 
occurs,  it  must  be  understood  as  including  those  abstract  terms  which 
have  come  to  be  employed  as  common  terms. 


fi' 


H 


ri 


46 


RELATION  Of   THE  PREDICATE 


It 


Note  I. — Contrary  to  the  practice  of  most  logicians,  I 
have  discussed  the  heads  of  predicates  under  the  second 
part  of  Logic.     In  taking  this  course,  I  have  attempted  to 
restore  to  them  their  original  significance  in  the  works 
of  Aristode,  as  a  classification  of  the  predicates  in  their 
relation  to  the  subjects  of  propositions.     It  is   perhaps 
needless  to  add,  that  I  have  not  followed  implicitly  the 
Aristotelian  account,  or  in  all  cases  adopted  the  Aristo- 
telian  phraseology.     By  Porphyry,  the  schoolmen,  and 
their  successors  of  the  seventeenth  and  eighteenth  cen- 
turies, the  heads  of  predicables  were  regarded  as  a  classi- 
fication of  universals  in  their  relations  to  one  another, 
rather  than  with  reference  to  their  place  in  a  proposition, 
and  consequendy,  from  the  time  that  Logic  was  divided 
into  parts,  were  discussed  under  the  first  part.     Defini- 
tion and  division,  as  dependent  on  a  knowledge  of  genus, 
species,  and  differentia,  are  also  here  treated  under  the 
second  part  of  Logic,  though  they  are  ordinarily  discussed 
under  the  first. 

Note  2.— On  the  vexed  and  subtle  question  of  the 
Import  of  Propositions,  or,  as  it  is  sometimes  called,  the 
Theory  of  Predication,  the  student  may  be  referred  to 
Hobbes'  Computation  or  Logic,  ch.  iii.,  Mr.  Mill's  Logic, 
Bk.  I.  ch.  v..  Dr.  Mansel's  Prolegomena  Logica,  ch.  ii.', 
Sir  W.  Hamilton's  Lectures  on  Logic,  Lects.  viii.  and  xiii., 
and  Mr.  Mill's  Examination  of  Sir  W.  Hamilton's  PhilL 
sophy,  ch.  xviii.  The  view  I  should  adopt  may  be 
briefly  stated  as  follows:  wherever  the  predicate  is  a 
singular  or  collective   term,  or,   though   a  common   or 


TO   THE  SUBJECT  OF  A   PROPOSITION,        47 


abstract  term,  a  synonym  of  the  subject,  the  theory  of 
Hobbes,  that  the  predicate  is  a  name  of  the  same  things 
of  which    the   subject  is  a  name,  furnishes   a   sufficient 
account;    in   all   other    cases,   Hobbes'   theory   is   true, 
though   insufficient,   for,  where   the  predicate  is    an  at- 
tributive or  an  abstract  term  (not  being  a  synonym),  the 
predicate  also  asserts  or  denies  certain  attributes  of  the 
subject,  and  where  it  is  a  common  term  (not  being  a 
synonym),    not   only  are    certain    attributes   asserted   or 
denied  of  the   subject,  but   the  latter  is  referred  to  or 
excluded  from  the  group  of  individuals  denoted  by  the 
predicate.     Thus,  in  the  proposition  *  Socrates  is  the  son 
of  Sophroniscus,'  the  predicate  may  be  regarded  as  simply 
another  name  for  the  subject ;  but  when  we  say  *  Socrates 
is  human,'  we  imply  more  than  this,  namely,  that  certain 
attributes  connoted  by  the  word  'human'  may  be  affirmed 
of  Socrates.     Further,  when  we  say  *  Socrates  is  a  man,' 
we  not   only  assign   another   name  to  the   subject,  and 
predicate  of  it  certain  attributes,  but  we  also  include  it  in 
a  certain  group.    This  peculiarity  follows  from  the  double 
signification  of  common  terms,  by  which  they  both  de- 
note a  group  of  individuals  and  connote  a  group  of  attri- 
butes, or,  in  other  words,  simultaneously  suggest  to  the 
mind  a  group  of  individual  objects  and  a  bundle  of  attri- 
butes characteristic  of  that  group.     From  what  has  been 
said  it  will  be  seen  that  I  do  not  agree  with  Mr.  Mill 
in  regarding  all  predication,  other  than  that  of  a  singular 
or  collective  term,  as  a  predication  merely  of  attributes. 


«! 


v\ 


i 


CHAPTER  VI. 
On   Verbal  and  Real  Propositions. 

AFFIRMATIVE  propositions  in  which  the  subject  is 
a  common  or  abstract  term  may  be  divided  into  Verbal 
and  Real.  A  verbal  proposition  expresses  merely  the 
connotation  or  part  of  the  connotation  of  the  term,  a 
real  proposition  expresses  either  solely,  or  in  conjunc- 
tion with  part  of  the  connotation  of  the  term,  properties, 
accidents,  or  both.  Thus  a  verbal  proposition  simply 
states  what  might  be  gathered  from  a  due  consideration 
of  the  name,  as  '  All  men  are  rational,'  *  All  triangles  are 
three-sided ' ;  whereas  a  real  proposition  imparts  know- 
ledge which  could  not  be  gathered  from  the  name  alone, 
as  *  All  triangles  have  the  sum  of  their  angles  equal  to 
two  right  angles,'  *  Some  men  are  black.'  It  is  plain  that 
all  particular  affirmative  propositions  are  real. 


iVd?/^.— The  distinction  between  verbal  and  real  propo- 
sitions is  otherwise  expressed  by  that  between  Analytical 
and  Synthetical  judgments  (Kant),  Explicative  and  Ampli- 
ative  judgments  (Sir  W.  Hamilton  and  Abp.  Thomson), 
Essential  and  Accidental  propositions  (the  schoolmen)! 
Tautologous  propositions  (All  A  is  A),  and  propositions 
in  which  the  predicate  is  a  synonym  of  the  subject  (as 
e.  g.  '  Charity  is  love '),  should  be  referred  to  the  head  of 
verbal  propositions. 


•  CHAPTER   VII. 
On  Definitions, 

A  DEFINITION  is  an  exposition  of  the  connotation 
of  a  term.  It  may  always  be  represented  in  the  form  of 
a  proposition,  of  which  the  term  defined  forms  the  subject 
and  the  exposition  the  predicate  ^ 

As  a  definition  expounds  or  enumerates  the  attributes 
which  a  term  implies,  it  is  plain  that  singular  and  collec- 
tive terms,  inasmuch  as  they  do  not  in  themselves  con- 
note any  attributes,  are  incapable  of  definition.  They  may, 
however,  be  described  by  means  of  the  various  common 
terms  which  are  predicable  of  them,  as  well  as  by  desig- 
nations which  are  peculiar  to  themselves.     Thus  I  may 
say  '  John  is  a  tall  man  of  fair  complexion,  is  by  profes- 
sion a  London  solicitor,  and  occupies  such  and  such  a 
house  in  Bedford-row.'     This  may  be  called  a  Description 
of  a  Singular  or  Collective  Term,  in  order  to  distinguish  it 
from  the  Description  of  a  common  term,  which  is  noticed 
below,  and  which  I  shall  call  simply  Description.    Besides 
singular  and  collective  terms,  a  term  expressing  a  single 
attribute,  which  is  incapable  of  analysis  into  other  attri- 
butes, is  incapable  of  definition.     Thus  it  has  been  main- 
tained that  it  is  useless  to  attempt  to  define  such  terms 
as  pleasure,  pain,  colour,  thing,  attribute,  &c. 

1  It  is  indifferent  whether  we  speak  of  the  entire  proposition  as  the 
definition,  or  merely  the  exposition  which  forms  the  predicate; 
similarly  in  the  case  of  a  description. 

£ 


50 


DEFINITIONS. 


DEFINITIONS, 


51 


In  defining  a  term,  it  would  of  course  be  impossible, 
in  every  case,  to  state  the  definition  in  terms  expressive 
of  attributes  which  are  themselves  incapable  of  analysis, 
even  if  we  were  agreed  as  to  what  are  terms  of  this 
character.  The  terms  employed  in  the  definition  may 
therefore  express  groups  of  attributes,  provided  that, 
when  taken  together,  they  exhaust  the  connotation  of 
the  term  defined.  Thus  each  of  the  terms  'under  one 
supreme  head '  and  *  political  government '  expresses  a 
large  group  of  attributes,  but  if,  when  taken  together, 
they  exhaust  the  connotation  of  the  word  'monarchy,' 
the  definition  may  be  accepted  as  legitimate. 

In  seeking  to  define  a  term,  I  invariably  contrast  it 
with  some  other  term;  often,  when  I  imagine  it  to  be 
difficult  to  exhaust  the  connotation,  with  a  variety  of 
other  terms,  from  which  I  seek  to  distinguish  it.  Thus 
in  seeking  to  define  '  monarchy,'  I  contrast  it  with  other 
forms  of  government ;  in  seeking  to  define  '  plane  triangle/ 
I  contrast  it  not  only  with  other  rectilineal  figures  but  with 
spherical  triangles ;  in  seeking  to  define  '  light,'  I  contrast 
it  with  heat,  sound,  electricity,  and  other  impalpable 
powers  of  nature.  Now  that  portion  of  the  definition 
which  is  common  to  the  term  defined  and  to  the  other 
terms  with  which  it  has  been  compared  is  called  the 
genus,  the  term  defined  standing  to  it  in  the  relation  of 
a  species,  as  has  already  been  explained;  that  portion 
which  distinguishes  the  term  defined  from  the  terms  with 
which  it  has  been  compared  is  called  the  differentia,  or 
sometimes,  when  there  is  more  than  one  distinguishing 


attribute,  the  differ  entice'^.  Thus,  if  we  were  distinguish- 
ing  rectilineal  triangle  from  spherical  triangle,  'three- 
sided  figure '  would  be  the  genus  ;  if  from  other  rectilineal 
figures,  the  genus  would  be  'rectilineal  figure';  if  from 
both  spherical  triangles  and  other  rectilineal  figures,  the 
genus  would  be  simply  '  figure.'  It  will  be  observed  that 
the  genus  is  always  expressed  in  the  form  of  a  common 
term,  or  of  an  abstract  term  which  is  used  as  a  common 
term,  and  that  it  may  be  qualified  by  an  attributive. 
This  is  the  case  even  in  defining  abstract  terms,  as  e.  g. 
in  the  definitions,  '  Justice  is  a  virtue  which  respects  our 
relations  to  other  men  in  society,'  '  Temperance  is  a 
virtue  which  respects  the  control  of  our  own  desires,'  the 
genus ^  is  'a  virtue,'  an  abstract  term  which  has  come 
to  be  used  as  a  common  term. 

A  Definition  being  an  exposition  of  the  meaning 
of  a  term,  it  is  obvious  that  all  definitions  must  be 
limited  by  the  state  of  our  knowledge  at  the  time  when 
we  frame  them.  But  some  terms  have  been  expressly 
framed  or  have  been  appropriated  to  express  a  small 
number  of  attributes.     Such  terms  are  monarchy,  anarchy, 

'  Some  Logicians  simply  use  the  word  '  differentia '  for  the  purpose 
of  expressing  the  distinguishing  attributes,  whether  one  or  many ; 
others,  as  Aristotle,  wpuld  in  the  latter  case  speak  of  the  *  differentiae.' 

*  Whenever  abstract  terms  are  defined  or  divided,  or  occur  as  por- 
tions of  definitions  or  divisions,  they  seem  invariably  to  be  treated  as 
if  they  were  common  terms,  and  hence  in  the  definitions  of  abstract 
terms,  as  in  other  definitions,  the  term  defined  may  be  regarded  as  a 
species ;  for  the  same  reason,  when  an  abstract  term  is  divided,  its 
relation  to  the  dividing  members  may  be  described  as  that  of  genus 
to  species. 

E  2 


:f 


5a 


DEFINITIONS. 


DEFINITIONS. 


53 


triangle,  square,  school,  monastery,  &c.  Our  accepted 
definitions  of  these  terms  we  may  be  quite  sure  we  shall 
not  be  compelled  to  alter  with  advancing  knowledge, 
provided  at  least  that  they  continue  to  denote  the 
same  objects.  But  however  full  and  adequate  to  our 
present  state  of  knowledge  our  definitions  of  man,  animal, 
vegetable,  light,  heat,  &c.,  might  be  at  the  present  time, 
they  might,  two  hundred  years  hence,  become  most  in- 
adequate and  incomplete,  if  not  incorrect,  even  although 
the  terms  continued  to  denote  the  same  objects  or  sen- 
sations. We  might,  for  instance,  discover  the  mode 
of  transmission  of  light,  or  that  the  animal  world  was 
not  separated  from  the  vegetable  by  the  same  character- 
istics by  which  we  now  conceive  it  to  be,  and  henceforth 
these  discoveries  would  become  part  of  the  connotation 
of  the  words,  or  would  materially  alter  the  connotation. 
In  the  greater  number  of  cases,  therefore,  we  must  be 
content  to  regard  our  definitions  as  provisional  *. 

But  not  only  must  we  in  most  cases  be  content  with 
provisional  definitions;  we  must  often  be  content  with 
definitions  which,  measured  even  by  our  present  state 
of  knowledge,  are  incomplete.  It  would  often  be  most 
inconvenient,  when  it  is  required  simply  to  distinguish 
between  two  terms,  to  give  the  full  connotation  of  each. 

*  It  would  be  a  service  to  logicians  if  there  were  recognised  names 
by  which  to  distinguish  between  these  two  different  classes  of  defini- 
tions, viz.  the  definitions  of  terms  whose  connotation  is  limited,  and 
whose  definitions  are  therefore  final,  and  the  definitions  of  terms  whose 
connotation  is  unlimited,  and  whose  definitions  are  therefore  pro- 
visional. 


In  such  cases,  therefore,  it  is  regarded  as  practically  suffi- 
cient,  if  we  refer  the  terms  contrasted  to  their  common 
genus,  and  specify  a  sufficient  number  of  attributes  to 
distinguish  each  from  the  other.  Thus  in  the  often- 
quoted  example  of  definition,  *  Man  is  a  rational  animal,' 
it  would  be  absurd  to  suppose  that  *  rational '  and  '  animal ' 
exhaust  the  connotation  of  '  man,'  but  the  word  *  rational ' 
is  sufficient,  for  popular  purposes,  roughly  to  distinguish 
the  human  race  from  the  lower  animals  with  which  it  is 
generally  contrasted.  When  these  incomplete  definitions, 
as  they  are  called  (i.  e.  definitions  which  do  not  give  the 
complete  connotation  of  a  term),  are  once  admitted,  it  is 
obvious  that  our  definitions  of  the  same  term  may  vary 
indefinitely  according  to  the  particular  point  of  view  from 
which  we  make  them,  or  the  science  which  we  happen  to 
be  pursuing  at  the  time. 

An  exposition  of  a  term  which  gives  no  part  of  its 
connotation,  but  in  lieu  of  it  an  enumeration  of  pro- 
perties   and  accidents,   is    called    a  Description.     Thus 

*  Man  is  a  featherless  biped  ^ '  would  be  regarded  as  a 
description,  not  as  a  definition  of  man.     But  the  term 

*  description '  is  also  extended  to  those  cases  in  which 

properties   and  accidents  are  combined  with  a  portion 

of  the   connotation^  the   latter    being  usually   stated  as 

the  genus.     Thus  we  might  describe  horse  as  an  animal 

*  Here  the  attributive  *  biped,*  being  used  as  a  quasi-genus  (i.e.  a 
property  or  accident  which,  for  a  special  purpose,  is  employed  as  a 
genus),  is  stated  in  the  form  of  a  substantive.  This  particular 
example  of  a  description  is,  of  course,  absurd,  and  simply  serves  the 
purpose  of  roughly  distinguishing  men  from  birds. 


54 


DEFINITIONS. 


I 


I 


which  is  domesticated,  which  has  a  mane  and  a  tail, 
which  has  a  high  value  attached  to  it,  which  is  to  be 
found  in  Arabia  and  Europe,  &c.,  &c.;  or  we  may 
take  as  an  instance  of  a  description  Cuvier's  definition 
of  man,  as  a  mammiferous  animal  having  two  hands. 
The  latter  instance  is  sufficient  to  shew  that  a  description 
may  often  sen-e  the  purpose  of  distinguishing  the  term 
described  from  all  other  terms,  and  may  therefore  be 
quite  adequate  to  fulfil  the  purposes  of  a  definition  for 
any  special  object. 

From  what  has  been  said  it  will  be  seen  that  definitions 
and  descriptions  may  be  classified  as  follows : — 

(i)  A  definition  complete  and  final. 

(2)  Complete  (so  far  as  we  know),  but  provisional. 

(3)  Incomplete,  but  sufficient  to  distinguish  the  term 

defined  from  all  other  terms. 

(4)  Incomplete,  but  sufficient  to  distinguish  the  term 

defined  for  the  special  purpose  in  hand. 

(5)  A  description  only,  but  sufficient  to  distinguish  the 

term  described  from  all  other  terms. 

(6)  A  description  only,  but  sufficient  to  distinguish  the 

term  described  for  the  special  purpose  in  hand. 
Any  pretended  definition  or  description  which  does  not 
fulfil  one  of  these  conditions  must  be  rejected  as  having 
no  value  whatever.  In  testing  a  definition  or  description, 
we  should  at  once  reject  it  if  it  were  applicable  to  any 
other  term,  unless  we  were  expressly  told  that  it  was 
used  only  for  the  purposes  of  a  particular  science,  and 
we  found  on   investigation  that  it  was  distinguishable 


DEFINITIONS. 


55 


from  all  other  terms  employed  in  that  science.  Thus, 
in  a  discussion  on  politics,  it  would  be  sufficient  to 
define  monarchy  as  the  supreme  government  of  one 
man,  but,  if  speaking  generally,  I  must  add  '  in  a  state,' 
for  one  man  may  be  supreme  governor  in  his  family,  in  a 
school,  in  a  religious  association,  &c. 

The  rules  for  a  legitimate  definition  must  depend  on 
the  kind  of  definition  which  we  purpose  or  are  compelled 
to  employ.  The  following  rules  are  common  to  the  three 
first  kinds  of  definition  enumerated  above : — 

1.  The  definition  must  be  convertible  with  the  term  de- 

fined, i.e.  it  must  apply  to  every  object  denoted 
by  the  term  defined,  and  to  no  other  objects. 

2.  The  definition  must  consist  of  one  common  term 

or  abstract  term  employed  as  a  common  term 
(the  genus),  and  of  one  or  more  attributives  (the 
differentia  or  differentiae). 

3.  Each   of  these  terms,  constituting   the    definition, 

must  connote  less  than  the  term  defined;  other- 
wise, they  afford  no  explication  of  it. 

4.  Each  of  these  terms  must  have  a  connotation  distinct 

from  that  of  the  others ;  otherwise,  the  definition 
will  be  redundant. 


I 


]\^^ote  I. — It  may  have  occurred  to  the  student  to  ask 
*  How  are  we  to  distinguish  those  attributes  which  form 
part  of  the  connotation  of  a  term,  from  the  attributes 
which   are  inferred   from   them?'     This   is  a   question 


5^ 


DEFINITIONS. 


which  in  many  individual  cases  it  would  be  extremely 
difficult  to  answer,  and  there  might  be  great  differences 
of  opinion  as  to  what  attributes  were  to  be  regarded  as 
*  differentiae,  and  what  as  properties.  It  is  in  fact  the 
same  question  as  *  What  are  primary,  and  what  are 
derived  qualities?'  The  only  general  answer  that  can 
be  given  is  that,  wherever  one  attribute  or  quality  can 
be  inferred  from  another,  it  is  to  be  regarded  as  a 
derived  quality  or  a  logical  property,  and  that  all  those 
attributes  that  cannot  be  so  derived  are  to  be  regarded 
provisionally  as  an  assemblage  of  primary  qualities  or, 
in  logical  language,  the  connotation  of  the  term.  As 
our  knowledge  advances,  it  is  of  course  possible  that 
many  of  these  primary  qualities  may  be  resolved  into 
secondary,  i.e.  many  of  the  supposed  differentise  may  be 
resolved  into  properties. 

Note  2. — The  scholastic  logicians  distinguished  between 
real  and  nominal  definitions,  meaning  by  a  real  definition 
the  explication  of  the  nature  of  a  thing,  by  a  nominal 
definition  the  explication  of  the  meaning  of  a  term.  The 
first  would  give  an  answer  to  such  a  question  as  '  What 
is  man?'  the  second  to  such  a  question  as  'What  do  we 
mean  by  the  term  man  ? '  As  the  meaning  we  attach  to  a 
term  ought  exactly  to  correspond  with  our  knowledge  of 
the  primary  or  underived  attributes  of  the  thing,  this  dis- 
tinction is  now  usually  regarded  as  nugatory.  Mr.  Mill 
has  however  revived  the  expressions  '  real '  and  '  nominal ' 
definition  to  mark  a  distinction  between  those  definitions 
which  assume  or  imply  the  existence  of  the  object  defined 


DEFINITIONS. 


57 


and  those  which  carry  with  them  no  such  assumption  or 
implication.  '  All  definitions,'  he  says,  '  are  of  names  and 
of  names  only ;  but,  in  some  definitions,  it  is  clearly 
apparent  that  nothing  is  intended  except  to  explain  the 
meaning  of  the  word ;  while  in  others,  besides  explaining 
the  meaning  of  the  word,  it  is  intended  to  be  implied  that 
there  exists  a  thing  corresponding  to  the  word.'  Thus 
the  definition  of  a  '  horse'  or  a  '  triangle'  would  be  called 
a  real  definition,  that  of  a  *  centaur '  a  nominal  definition. 
See  Mill's  Logic,  Bk.  I.  ch.  viii.  s.  5. 

jSfote  3.— Sometimes  we  may  explain  a  term  by  a 
synonym,  an  etymology,  or  a  translation,  which  may 
accidentally  be  better  known  to  the  hearer  or  reader 
than  the  term  so  explained.  These  explanations  cannot 
be  accepted  as  definitions  in  our  sense  of  the  word,  inas- 
much as  they  do  not  analyse  the  connotation  of  the 
term;  but  they  would  have  been  regarded  as  instances 
of  nominal  definitions  by  the  older  logicians. 


CHAPTER  VIII. 
On  Divisions  and  Classifications. 

A  DIVISION  is  an  exposition  of  the  denotation  of 
a  term.  It  may  always  be  represented  in  the  form  of 
a  proposition,  of  which  the  term  divided  forms  the  subject 
and  the  exposition  the  predicate. 

In  divisions  the  denotation  of  a  term  is  expounded 
by  enumerating,  not  the  individuals  (which  would  in  most 
cases  be  impossible),  but  the  smaller  groups  which  the 
term  denotes.  The  terms  denoting  these  smaller  groups 
are  called  the  dividing  members  (niembra  divideniia)  in 
contradistinction  to  the  divided  term  (called  by  the  older 
logicians  the  '  divided  whole,'  totum  divisum). 

It  is  plain  that  common  terms,  or  abstract  terms  which 
are  employed  as  common  terms,  are  alone  capable  of 
being  divided.  Abstract  terms  and  attributives  have,  in 
themselves,  no  denotation,  while  singular  and  collective 
terms  are  incapable  of  being  divided  into  smaller  groups. 
A  collective  term  may  however  easily  be  transformed  into 
a  common  term,  and  so  rendered  capable  of  being  divided; 
thus  '  the  fourteenth  regiment '  may  become  '  soldiers  of 
the  fourteenth  regiment,'  and  in  this  form  may  be  divided 
into  officers  and  privates,  or  other  groups.  The  same 
remark  holds  good  of  abstract  terms  and  attributives. 


DIVISIONS  AND   CLASSIFICATIONS, 


59 


It  may  be  laid  down  as  a  test  of  a  logical  division  that 
the  term  divided  must  be  predicable  of  each  dividing 
member.  Thus  'figure'  is  predicable  aUke  of  triangle, 
square,  &c., '  man,'  of  white  man  and  black  man.  In  this 
manner  it  is  distinguished  from  partition  of  a  physical 
whole  into  its  parts,  as  of  '  man '  into  head,  arms,  legs,  &c., 
or  of  the  '  world'  into  Europe,  Asia,  Africa,  and  America. 
But  this  test,  though  sufficient  to  distinguish  a  division 
from  a  partition,  is  not  sufficient  to  distinguish  it  from 
two  other  forms  of  propositions,  which  nevertheless  we 
must  beware  of  confounding  with  it.  These  are  an 
enumeration  of  individuals,  and  a  distinction  of  an  equi- 
vocal term  according  to  its  various  meanings,  as  e.g.  of 
'humanity,'  according  as  it  means  human  nature,  the 
human  race  collectively,  the  virtue  of  being  humane,  or 
the  study  of  polite  letters.  In  a  distinction  the  same 
definition  is  not  predicable  of  each  of  the  terms  dis- 
tinguished, but  in  a  division  the  same  definition  is  pre- 
dicable of  each  dividing  member. 

In  dividing  a  term  into  terms  expressive  of  smaller 
groups  (or,  as  they  are  frequently  called,  subject  classes), 
I  invariably  try  to  think  of  some  attribute  which  is  pre- 
dicable of  certain  members  of  the  group,  but  not  of 
others.  This  attribute  suggests  what  is  called  the/««- 
damentum  divisionis  or  principle  of  division  (i.  e.  some 
character  of  the  group,  which  is  a  source  of  differ- 
ences amongst  its  members).  Thus,  if  asked  to  divide 
'  triangles,'  it  may  first  occur  to  me  that  some  triangles 
have    equal    sides    and    others   not;    in  this  case   the 


6o 


DIVISIONS  AND   CLASSIFICATIONS, 


DIVISIONS  AND   CLASSIFICATIONS, 


61 


property  of  a  triangle  that  the  lengths  of  its  sides  may 
be  variously  related,  or,  in  other  words,  the  relation 
of  the  sides,  becomes  the  fundamentum  divisionis,  and 
I  divide  triangles  into  equilateral,  isosceles,  and  scalene. 
Or  it  may  first  occur  to  me  that  some  triangles  are  right- 
angled,  and  others  not ;  in  this  case  the  measure  of  the 
angles  becomes  the  fundamentum  divisionis,  and  I  divide 
triangles  into  right-angled,  obtuse-angled,  and  acute- 
angled.  Or,  to  take  one  more  instance,  if  asked  to  divide 
*  governments,*  I  may  reflect  that  in  some  governments  the 
sovereignty  is  divided,  in  others  it  is  placed  entirely  in  the 
hands  of  one  person  or  order,  and  I  may  divide  '  govern- 
ments '  accordingly  into  pure  and  mixed,  proceeding  to 
divide  pure  governments,  according  to  the  number  of 
persons  in  whose  hands  the  sovereignty  is  placed,  into 
monarchies,  oligarchies,  and  democracies.  Any  division 
in  which  two  or  more  fundamenta  divisionis  are  con- 
founded^, or  cut  across  one  another,  is  called  a  cross- 
division  and  is  logically  inadmissible.  Thus  a  division 
of  triangles  into  isosceles,  scalene,  and  right-angled,  or  of 
governments  into  monarchies,  free  governments,  and 
mixed  governments,  or  of  men  into  Frenchmen,  Asiatics, 
the  unproductive  classes,  and  barbarians,  would  be  a 
cross-division.  In  the  last  example  there  is  a  confusion 
of  no  less  than  four  fundamenta  divisionis. 

It  is  maintained  by  many  logicians,  and  with  justice, 

^  But,  as  in  Natural  Classifications  (see  p.  62  below),  we  may  employ 
any  number  of  fundamenta  divisionis,  provided  that  their  results 
coincide. 


that  in  every  legitimate  division  (or,  at  least,  in  every 
division  which  we  have  sufficient  reason  for  knowing 
to  be  legitimate),  the  process  by  which  the  division  is 
arrived  at,  if  strictly  analysed,  may  be  described 'as  follows. 
Taking,  for  instance,  '  triangles,'  we  reflect,  say,  that  some 
are  equilateral;  we  then  divide  triangles  into  equilateral 
and  those  which  are  not  equilateral,  and  again,  still  think- 
ing of  equality  of  sides,  those  which  are  not  equilateral 
into  those  which  have  two  sides  equal  (isosceles),  and 
those  which  have  none  (scalene).  Similarly,  taking  *  men,' 
and  thinking  of  race  as  our  fundamentum  divisionis, 
we  divide  mankind  into  Aryans  and  those  who  are  not 
Aryans,  the  latter  into  Semites  and  those  who  are  not, 
the  latter  into  Turanians  and  those  who  are  not,  and 
so  on,  till  our  division  is  complete.  This  process,  when 
formally  drawn  out,  is  called  Division  by  Dichotomy,  and 
the  rule  by  which  it  proceeds  is  in  each  division  to  take 
two  terms  which  admit  no  medium  between  them.  Thus 
such  pairs  of  terms  as  productive  and  unproductive, 
fallible  and  infallible,  white  and  not  white,  would  answer 
the  purpose. 

The  divided  term  stands  of  course  to  the  dividing 
members  as  a  genus  to  species.  We  can  also  gather 
the  differentia  froih  the  fundamentum  divisionis.  Thus, 
in  dividing  a  term,  we  virtually  define  the  subject  terms. 
A  pure  government,  for  instance,  may  be  defined  as  a 
government  in  which  the  sovereignty  is  undivided,  and 
a  mixed  government  as  a  government  in  which  the 
sovereignty  is  divided.     In    defining   also  we   virtually 


62 


DIVISIONS  AND   CLASSIFICATIONS, 


divide.  Thus  the  definition  of  man  as  a  rational  animal 
implies  a  division  of  animals  into  men  and  brutes,  and 
the  definition  of  a  plane  triangle  as  a  three-sided  recti- 
lineal figure  implies  a  division  of  rectilineal  figures  into 
three-sided  and  not  three-sided  (i.  e.  quadrilaterals  and 
polygons). 

The  rules  for  a  legitimate  division  may,  in  accordance 
with  what  has  already  been  said,  be  stated  as  follows : — 

1.  Each  dividing  member  must  be  a  common  term,  or 
an  abstract  term  which  is  used  as  a  common  term. 

2.  The  divided  term  must  be  predicable  of  each  divid- 
ing member. 

3.  The  division  must  be  exhaustive,  i.e.  the  dividing 
members,  when  taken  together,  must  be  equal  in  extent 
to  the  term  divided. 

4.  The  dividing  members  must  be  mutually  exclusive, 
i.  e.  no  subordinate  species  must  be  included  under  more 
than  one  of  them ;  otherwise  we  have  a  cross-division. 

The  surest  mode  of  satisfying  the  last  condition  is  to 
employ  only  one  fundamentum  divisionis,  and  in  artificial 
classifications  this  method  is  adopted,  but  it  is  the  dis- 
tinctive characteristic  of  natural  classifications,  which 
alone  are  adequate  to  many  of  the  purposes  of  science, 
to  employ  simultaneously  a  number  of  principles  of  divi- 
sion. (See  Inductive  Logic,  ch.  ii.  §  2  (i),  4th  ed.  pp. 
50-74.)  In  the  latter  case,  therefore,  the  observation  of 
this  rule  becomes  a  most  important  check  on  unskilful 
classification  '^. 

*  In  order  to  adapt  the  Rules  of  Division,  as  here  given,  to  the 


DIVISIONS  AND   CLASSIFICATIONS, 


63 


The  student  may  easily  frame  for  himself  examples  of 
illegitimate  divisions.  If  we  were  absurdly  to  divide 
Europeans  into  Celts,  Teutons,  Sclaves,  Frenchmen, 
Spaniards,  the  Emperor  of  Russia,  and  the  President 
of  the  United  States  of  America,  we  should  have  an 
example  of  all  the  faults  incident  to  a  division. 

In  speaking  of  division  by  dichotomy  I  have  already 
introduced  the  notion  of  sub-division.  For  scientific 
accuracy,  and  often  even  for  practical  purposes,  it  may 
be  necessary  to  sub-divide  the  dividing  members,  again 
to  sub-divide  the  results  of  this  division,  and  so  on. 
The  relation  of  these  various  divisions  and  sub-divisions, 
one  to  another,  has  given  rise  to  several  logical  terms, 
and  is  of  sufficient  importance  in  itself  to  require  a  brief 
treatment.  It  is  best  to  commence  with  an  example, 
and  I  select  a  mathematical  one,  as  being  of  the  simplest 

kind : — 

Figure. 


Curvilinear. 


Rectilinear. 
I 


Triangle.         Quadrilateral. 
I . 


1 

Polygon. 


Equilateral. 


Isosceles. 


Scalene. 


In  a  series  of  divisions  and  sub-divisions  like  the  fore- 
going, the  term  at 'the  head  of  the  series  (in  this  case 
Figure)  is  called  the  Summum  Genus.  The  terms  at  the 
bottom  of  the  series  (equilateral  triangles,  circles,  &c.) 

Natural  Classifications  of  Science  as  well  as  to  the  Artificial  Classifi- 
cations of  ordinary  life,  an  important  change  has  been  made  in  the 
statement  of  Rule  4  in  the  later  editions  of  this  work. 


f' 


'  M 


64 


DIVISIONS  AND   CLASSIFICATIONS, 


are  called  Infimce  Species.  The  intermediate  terms  are 
called  Subaltern  Genera,  or  Subaltern  Species,  viz.  sub- 
altern genera  with  reference  to  the  terms  immediately 
below  them,  and  subaltern  species  with  reference  to  the 
terms  immediately  above  them.  Thus  triangle  would  be 
a  subaltern  genus  with  reference  to  equilateral  triangle, 
a  subaltern  species  with  reference  to  rectilinear  figure. 
Species  which  fall  immediately  under  the  same  genus,  as 
e.  g.  triangle,  quadrilateral,  and  polygon,  are  sometimes 
called  Cognate  Species,  but  might,  perhaps,  with  greater 
propriety  be  called  Co-ordinate  Species.  A  Cognate  Genus 
is  any  one  of  the  ascending  genera  under  which  the 
species  falls.  Thus  triangle,  rectilinear  figure,  figure,  are 
all  genera  cognate  to  equilateral  triangle.  A  differentia 
which  constitutes,  as  is  said,  the  species  of  which  we 
happen  to  be  speaking,  that  is,  which  distinguishes  it 
from  its  co-ordinate  species,  is  called  a  Specific  Difference, 
one  which  constitutes  any  of  its  cognate  genera  is  called 
a  Generic  Difference.  Thus  *  equilateral '  is  a  specific 
difference,  '  three-sided '  a  generic  difference  of  an  equi- 
lateral triangle.  Or,  *  three-sided  *  would  be  regarded  as 
a  specific  difference,  and  *  rectilinear '  a  generic  difference 
of  a  triangle.  Lastly,  a  property  derived  from  an  attri- 
bute or  attributes  connoted  by  the  species  of  which  we 
happen  to  be  speaking  is  called  a  Specific  Property,  a 
property  which  is  derived  from  any  of  its  cognate  genera 
is  called  a  Generic  Property.  It  is,  for  instance,  a  pro- 
perty of  all  rectilineal  figures  that  the  sum  of  their  angles 
is  equal  to  twice  as  many  right  angles  as  the  figure  has 


DIVISIONS  AND    CLASSIFICATIONS. 


65 


sides,  minus  four  right  angles.  Thus  the  angles  of  a 
plane  triangle  are  together  equal  to  two  right  angles, 
those  of  a  quadrilateral  to  four,  those  of  a  pentagon  to 
six,  and  so  on.  It  is  also  a  property  of  a  triangle  that 
it  may  be  generated  by  the  section  of  a  cone,  but  this 
is  not  a  property  common  to  other  rectilinear  figures. 
Hence  the  latter  would  be  called  a  specific,  the  former 
a  generic  property. 

The  instance  I  have  given  is  one  of  the  simplest  that 
could  be  selected.  If  I  had  taken  instead  of  it,  say, 
the  division  of  animals  into  vertebrate  and  invertebrate, 
of  vertebrate  animals  into  fishes,  amphibia,  reptiles,  birds, 
and  mammals,  of  mammals  into  the  various  species  of 
men,  horses,  oxen,  &c.,  it  would  have  required  a  long 
scientific  discussion  to  distinguish  the  various  species  and 
genera,  to  state  the  specific  and  generic  differences,  and 
to  give  instances  of  specific  and  generic  properties.  And 
yet  it  is  exactly  in  such  a  case  as  this  that  divisions  and 
sub-divisions  (or,  in  one  word,  Classifications)  are  most 
important.  In  fact,  the  sciences  of  Botany  and  Zoology 
(in  the  vulgar  acceptation  of  these  words)  consist  en- 
tirely of  classifications.  To  give  rules  for  so  important 
and  complicated  a  process  as  scientific  classification, 
or  even  to  attempt  any  precise  definition  of  the  word, 
would  be  to  go  beyond  the  scope  of  an  elementary 
work  like  this^  It  may  be  sufficient  to  suggest  that 
where,  as  in  the  case  of  plants  and  animals,  species  are 

s  The  reader  will  find  a  special  section  on  Classification  in  the 
Author's  *  Elements  of  Inductive  Logic* 

F 


\\ 


ii 


( ' 


66 


DIVISIONS  AND    CLASSIFICATIONS. 


DIVISIONS  AND    CLASSIFICATIONS, 


67 


separated  from  one  another  by  an  indefinite  number  of 
attributes,  and  may  be  separated  by  many  attributes  of 
which  we  are  still  ignorant,  our  classifications,  like  our 
definitions,  should  always  be  regarded  as  provisional. 
To  this  I  may  add  two  plain  rules,  which  meet  with 
universal  acceptance :  first,  that  our  classifications  should 
proceed  as  gradually  as  possible;  and  second,  that  we 
should  select  as  our  main  principles  of  division  attributes 
the  most  fruitful  in  their  consequences,  i.e.  attributes  from 
which  the  largest  number  of  important  properties  can  be 
derived*.  Thus  the  natural  system  of  Botany,  founded, 
in  its  main  division,  on  differences  in  the  seed-vessels 
of  plants,  is  far  more  instructive  than  the  Linnaean  system, 
founded  on  differences  in  the  numbers  of  the  pistils  and 
stamens. 

Note. — I  have  employed  the  expressions  '  summum 
genus '  and  '  infima  species,'  as  if  they  were  entirely  rela- 
tive to  any  particular  classification.  But  in  the  Isagoge 
of  Porphyry,  and  by  the  Scholastic  logicians  who,  for 
the  most  part,  adopted  his  account,  both  summa  genera 
and  infimae  species,  as  well  as  all  the  subaltern  genera  and 
species,  were  regarded  as  unalterably  fixed  by  nature. 
Thus  the  ten  Categories  of  Aristotle  (Substance,  Quan- 
tity, Quality,  Relation,  &c.)  were  regarded  as  the  summa 
genera,  and  terms  like  man,  horse,  &c.  were  regarded  as 

*  Such  attributes  are  called  by  the  French  physiologists  caradlres 
dominateurs.  See  Milne  Edwards,  Cou>s  Element  aire  de  Zoologie, 
edition  septieme,  §  367. 


expressing  infimae  species.  Classes  like  'black  men,' 
'Arabian  horses,'  &c.  would  not  have  been  admitted  to 
be  species  at  all.  We,  on  the  contrary,  conceive  that 
there  is  no  limit  to  our  power  of  making  classes ;  how- 
ever specialised  a  group  may  be,  we  can  almost  always 
think  of  some  attribute,  the  addition  of  which  will  make 
it  more  special  still. 


: 
I 


fe»-3*A;'*^>=S» 


F  2 


VARIOUS  KINDS  OF  INFERENCES. 


69 


PART    III.— Of  Inferences. 

CHAPTER   I. 
On  the  VarioiLs  Kinds  of  Inferences. 

THE  third  and  most  important  part  of  Logic  treats 
of  Inferences  *.  Wherever  we  assert  a  proposition  in  con- 
sequence of  one  or  more  other  propositions,  or,  in  other 
words,  wherever  we  regard  one  or  more  propositions  as 
justifying  us  in  asserting  a  proposition  distinct  from  any 
that  has  preceded,  the  combination  of  propositions  may 
be  regarded  as  an  inference.  Thus  defined,  inferences 
may  be  divided  into  inductive  and  deductive,  and  de- 
ductive inferences  may  be  sub-divided  into  mediate  and 
immediate.  I  shall  attempt  to  make  these  distinctions 
clear  by  examples. 

^  The  word  *  inference '  is  employed  in  no  less  than  three  different 
senses.  It  is  sometimes  used  to  express  the  conclusion  in  conjunction 
with  the  premiss  or  premisses  from  which  it  is  derived,  as  when  we 
speak  of  a  syllogism  or  an  induction  as  an  inference  ;  sometimes  it  is 
used  to  express  the  conclusion  alone ;  sometimes  the  process  by  which 
the  conclusion  is  derived  from  the  premisses,  as  when  we  speak  of 
Induction  or  Deduction  as  inferences  or  inferential  processes.  Except 
where  the  meaning  is  obvious  from  the  context,  I  shall  endeavour  to 
confine  the  word  to  the  first-named  signification.  The  terms  Induc- 
tion and  Deduction  will  be  appropriated  to  express  processes  which 
result,  the  former  in  inductiofis  or  inductive  inferences,  the  latter  in 
deductions  or  deductive  infereiues,  these  last  being  sub-divided  into 
syllogisms  and  immediate  inferences. 


I  mix  tartaric  acid  and  carbonate  of  soda*  in  certain 
proportions  in  water,  and  I  observe  that  the  mixture  is 
followed  by  an   effervescence;    from  this  I   infer  that, 
whenever  tartaric  acid  and  carbonate  of  soda  are  mixed 
in  water  in  these  proportions,  effervescence  will  follow. 
I  put  a  poker  into  the  fire,  and  I  observe  that  after  a  time 
it  becomes  red-hot ;  from  this  I  infer  that  incandescence 
can  always  be  produced  in  iron  by  a  certain  degree  of 
heat.     I  observe  five  points  in  the  orbit  of  a  planet,  and, 
from  my  knowledge  of  mathematics,  perceive  that  they 
are  situated  in  an  ellipse :  from  this  I  infer  that  the  entire 
orbit  of  the  planet   is  elliptical,  and  that,  in  all  future 
revolutions  of  the  planet,  a  similar  orbit  will  be  described. 
Now  what  in  these  cases  do  I  mean  by  the  word  '  infer  ? ' 
That  the  mixture  is  followed  by  effervescence  is  a  matter 
of  observation ;  but  it  is  only  an  inferential  process  which 
justifies  me  in  asserting  that,  inasmuch  as  it  could  have 
been  produced  by  nothing   else,  the   effervescence  was 
produced  by  the  mixture,  and  that,  whenever  in  future  I 
see  a  similar  mixture,  I  may  expect  to  see  it  followed  by 
similar  results.     Two  assumptions,  it  will  be  seen,  under- 
lie this  inference  :   ist,  that  every  event  has  a  cause,  which 
leads  me  to  assume  that  the  effervescence  must  have  been 
produced  by  some  cause  or  other;  2nd,  the  belief  in  the 
uniformity   of   nature,  which  leads   me  to   expect   that, 
whenever  similar  circumstances   are  repeated,  they  will 
be  followed  by  similar  results.     The  reasoning  therefore 
in  these  cases  may  be  represented  as  follows : — 

The  mixture  of  the  tartaric  acid  with  the  carbonate 


70 


VARIOUS  KINDS  OF  INFERENCES, 


VARIOUS  KINDS  OF  INFERENCES. 


71 


of  soda  is  followed  by  effervescence.      (Original 
Proposition.) 

.-.  (Owing  to  the  special  circumstances  of  the  case  and 
in  accordance  with  the  principle  that  every  event 
must  have  a  cause),  the  effervescence  was  produced 
by  the  mixture. 

.-.  (In  accordance  with  the  principle  of  the  uniformity 
of  nature),  a  similar  mixture  will  always  be  fol- 
lowed by  an  effervescence. 

We  may  represent  the  reasoning  in  the  third  example 
in  the  same  manner : — 

We  may  assert  (by  virtue  of  our  knowledge  of 
mathematics)  that  five  points  which  we  have  ob- 
served in  the  orbit  of  the  planet  Mars  are  situated 
in  the  arc  of  an  ellipse.     (Original  Proposition.) 

.•.As  there  are,  comparatively  speaking,  no  causes  de- 
termining the  position  of  the  planet  at  any  given 
moment,  except  the  attraction  of  the  sun  and  the 
continued  effects  of  the  initial  velocity,  we  may 
infer  that  the  fact  of  the  five  points  observed  being 
situated  in  the  arc  of  an  ellipse  is  due  to  the  com- 
bination of  these  two  causes. 

.*.  (In  accordance  with  the  principle  of  the  uniformity 
of  nature),  it  may  be  inferred  that  all  other  points 
in  the  orbit  of  the  planet  are  situated  in  an 
ellipse,  and  that,  in  all  future  revolutions,  a  similar 
orbit  will  be  described ;  i.  e.  the  orbit  of  the  planet 
Mars  may  be  regarded  as  elliptical. 


Now  inferences  of  this  kind  are  called  IndMive.     The 
instances   I   have   selected   are   remarkably   simple,  but 
they  are   sufficient   to   shew  that  an  induction  may  be 
defined  as  an  inference  in  which  we  argue  from  parti- 
culars to   adjacent  particulars,  or   (if  we   speak   of  the 
adjacent  particulars  collectively)  from  particulars  to  uni- 
versals,  in  accordance  with  the  laws  of  universal  causation 
and  of  the  uniformity  of  nature.    As  to  the  circumstances 
which  justify  us  in  asserting  that  one  phenomenon  or  set 
of  phenomena  is  the  cause  or  the  effect  of,  or  is  invariably 
conjoined  with,  another  (for  this  is  the  problem  of  Induc- 
tion), the  student  is  referred  to  works  specially  treating  of 
Inductive  Inference.     It  is  sufficient  here  to  distinguish 
inductive  from  the  deductive  inferences  which  it  is  our 
more  special  business  to  explain  2. 

2  An  Analogy  is  a  form  of  imperfect  induction,  and,  though  justify- 
ing a  conclusion  more  or  less  probable,  never  leads  to  certainty.     If 
two  objects  resemble  each  other  in  several  important  respects,  and 
we  argue  that  any  particular  attribute  which  we  know  to  be  predicable 
of  the  one,  and  do  not  know  to  be  either  predicable  or  not  predicable 
of  the  other,  is,  on  account  of  the  general  resemblance  of  the  two 
objects,  also  predicable  of  the  other,  the  argument  is  called  an  argu- 
ment from  analogy ;  and,  in  the  same  way,  if  two  objects  are  dis- 
similar, we  may  argue  that  an  attribute  which  is  predicable  of  the 
one,  is,  on  account  of  their  dissimilarity,  not  predicable  of  the  other 
Thus,  from  the  similaVity  between  the  earth  and  the  moon,  we  might 
argue  that  the  latter  is  inhabited,  or,  from  their  dissimilarity,  that  it 
is  not  inhabited.     The  value  of  the  inference  always  depends  on  the 
ratio  of  the  ascertained  resemblances  to  the  ascertained  differences 
(it  being  understood  that  the  resemblances  which  we  take  into  account 
are  none  of  them  derived,  as  properties,  from  each  other,  and  so  with 
the  differences),  providing  that  our  knowledge  of  the  objects  is  suf- 
ficiently large  to  justify  us  in  drawing  any  inference  at  all.  For  a  more 


72 


VARIOUS  KINDS  OF  INFERENCES, 


VARIOUS  KINDS  OF  INFERENCES, 


73 


Beginning  where  induction  ended,  we  may  state  such 
a  proposition  as  this:  'All  iron  when  heated  to  a  cer- 
tain degree  becomes  red-hot.'  This,  if  combined  with 
another  proposition  '  This  is  a  piece  of  iron,'  leads  to  the 
conclusion  '  This  piece  of  iron,  if  heated  to  a  certain 
degree,  will  become  red-hot/  Now  it  is  plain  that  the  con- 
detailed  analysis  of  this  mode  of  reasoning,  and  an  estimate  of  the 
value  to  be  attached  to  its  conclusions,  the  student  is  referred  to  the 
author's  Elements  of  Inductive  Logic,  ch.  iv.,  and  to  Mr.  Mill's  Z^^V, 
Bk.  III.  ch.  XX.,  one  of  the  most  instructive  and  important  chapters 
in  his  work. 

It  should  be  noticed  that  an  analogy,  as  here  described,  is  not 
identical  with  the  Analogy  of  Aristotle,  the  Aristotelian  Analogy 
being  an  equality  of  relations  (tVoxT^s  A(>7£yi/).     Thus  the  expression. 

The  intellect :  the  soul  =  the  sight  :  the  body, 
is  an  avako-^ia.     From  this  analogy  it  is  argued  that  anything  which 
may  be  predicated  of  the  one  pair  of  terms  may  be  predicated  also  of 
the  other.     Or,  to  take  a  non-Aristotelian  instance,  which  will  be 
more  intelligible  to  beginners : 

A  colony  :  the  mother-country  =  a  child  :  a  parent. 
From  this  analogy  it  is  argued  that  the  reciprocal  rights  and  duties 
of  a  colony  and  the  mother-state  are  the  same  as  those  of  a  child  and 
a  parent.  In  this  form  of  argument,  if  the  relations  between  the  two 
sets  of  terms  were  precisely  the  same  in  all  respects,  the  conclusion 
would  be  invariably  valid ;  as  it  is  usually  found  in  practice,  how- 
ever, the  relations  are  the  same  in  some  respects,  but  not  in  others, 
and,  consequently,  the  conclusion  is  valid,  when  based  on  those 
points  in  which  the  relations  are  the  same,  and  invalid,  when  based 
on  those  points  in  which  the  relations  are  not  the  same.  Thus,  it 
might  be  maintained  that,  in  many  respects,  the  relation  of  the  child 
to  the  parent  is  not  the  same  as  that  of  a  colony  to  the  mother- 
country,  and,  hence,  that  many  of  the  rights  and  duties  which  exist 
in  the  one  case  do  not  exist  in  the  other.  A  Metaphor  is  an  analogy 
of  this  kind  compressed  into  a  single  word  or  phrase. 
The  fallacy  of  False  Analogy  will  be  noticed  below. 


elusion  we  have  just  drawn  w^as  arrived  at  ill  a  different 
manner  from  those  noticed  above.  Instead  of  being  the 
conclusion  of  a  process  by  which  we  argue  from  parti- 
culars to  adjacent  particulars  or  from  particulars  to 
universals  (i.  e.  from  cases  which  are  within  the  range  of 
our  observation  to  others  which  are  without),  it  is  simply 
a  combination  of  two  propositions  into  one,  being  an 
obvious  inference  from  what  has  been  previously  stated 
in  the  premisses.  Induction  has  been  not  inaptly  com- 
pared to  the  establishing  of  a  formula,  Deduction  (for 
that  is  the  appropriate  name  of  the  process  which  I  am 
now  discussing)  to  the  reading  it  off.  Induction  leads 
to  truths  entirely  new.  Deduction  combines,  methodizes, 
and  developes  those  which  we  have  already  gained. 

A  Syllogism  may  be  called  a  Mediate  Inference, 
because  the  two  terms  of  the  conclusion  are  compared 
in  the  premisses  by  means  of  a  third.  It  is  thus 
opposed  to  an  Immediate  Inference,  which  consists  of 
two  propositions  only,  and  in  which  the  inferred  propo- 
sition is  derived  from  a  single  proposition  without  the 
aid  of  any  other  term  or  proposition,  expressed  or 
implied.  Both  mediate  and  immediate  inferences  may 
be  styled  deductive  as  opposed  to  inductive. 

This  division  may  easily  be  shewn  to  be  exhaustive.  In 
any  inference,  we  argue  either  to  something  already 
implied   in   the   premisses^   or   not;    if  the   latter,   the 

»  If  we  state  explicitly  all  the  assumptions  made  in  the  inductive 
process,  the  conclusion  is  contained  in  the  premisses,  and  the  form  of 
the  reasoning  becomes  deductive ;  but  it  is  seldom  that  wc  do  state 


74 


VARIOUS  KINDS  OF  INFERENCES. 


inference  is  inductive,  if  the  former,  deductive.  If  the 
deductive  inference  contain  only  a  single  premiss,  it  is 
immediate ;  if  it  contain  two  premisses  and  the  conclusion 
be  drawn  from  these  jointly,  it  is  mediate  and  is  called 
a  syllogism.  All  deductive  inferences  which  apparently 
contain  more  premisses  than  two  admit  of  being  analysed 
into  a  series  of  syllogisms. 


Nok  I. — I  am  here  departing  from  the  ordinary 
scheme  of  division  adopted  by  logicians.  Inferences  are 
generally  divided  into  mediate  and  immediate,  and  mediate 
inferences  are  subdivided  into  inductive  and  deductive.  As 
however  I  regard  inductions  as  more  strongly  contrasted 
with  both  syllogisms  and  immediate  inferences  than  either 
of  these  classes  is  with  the  other,  it  seems  preferable  to 
make  inductions  one  of  the  main  members,  rather  than 

our  assumptions  thus  explicitly.  The  most  essential  distinction, 
however,  between  inductive  and  deductive  reasoning  consists  not  in 
the  form  of  the  inferences,  but  in  the  nature  of  the  assumptions  on 
which  they  rest.  Deductive  reasoning  rests  on  certain  assumptions 
with  regard  to  language  and  co-existence  (namely,  the  so-called 
Law  of  Identity,  or  some  modification  of  that  law,  the  Law  of  Con- 
tradiction, the  Law  of  Excluded  Middle,  and  the  Canons  of  Syllogism), 
while  inductive  reasoning  assumes  over  and  besides  these  laws  the 
truth  of  the  Laws  of  Universal  Causation  of  the  Uniformity  of  Nature 
and,  in  certain  cases,  of  the  Conservation  of  Energy ;  or,  if  it  be  of 
the  unscientific  description  which  is  known  as  Inductio  per  Enumera- 
tionem  Simplicem,  it  merely  assumes,  instead  of  them,  the  vague  and 
wide  principle  that  the  unknown  resembles,  or  will  resemble,  the 
known.  It  hardly  needs  to  be  added  that  all  reasoning  alike  assumes 
the  trustworthiness  of  present  consciousness  and  of  memory. 


VARIOUS  KINDS  OF  INFERENCES,  75 

one  of  the  subordinate  members  of  the  division.  Nor  is 
there  any  reason  why  an  immediate  inference  should  not 
be  regarded  as  deductive. 

It  should  also  be  noticed  that  Sir  W.  Hamilton  would 
deny  the  title  of  inferences  to  inductions  (as  they  have 
been  here  explained),  whereas  Mr.  Mill  would  deny  that 
either  a  syllogism  or  an  immediate  inference  can  properly 
be  called  an  inference.  Mr.  Mill  maintains  that  all  In- 
ference is  '  from  the  known  to  the  unknown ' ;  Sir  W. 
Hamilton  defines  Inference  as  the  'carrying  out  into 
the  last  proposition  what  was  virtually  contained  in  the 
antecedent  judgments.' 

j^oie  2.— The  Aristotelian  induction,  in  which  the 
conclusion  affirms  or  denies  of  a  group  what  was  in  the 
premisses  affirmed  or  denied  of  each  member  of  the 
group  severally,  is,  according  to  the  above  method  of 
treatment,  obviously  regarded  as  a  deductive  inference. 
If  I  predicate  some  quality  of  each  member  of  a  group, 
and  thence  infer  that  all  members  of  the  group  possess 
this  quality,  the  conclusion  is  plainly  contained  in  the 
premisses,  and  the  inference  is  a  syllogism.  It  may  be 
represented  in  the  form  * — 

*  By  Aristode  himself  the  inductive  inference  is  analysed  thus  :  — 

x,  y,  z  are  B, 

X,  y,  z  are  (i.e.  constitute)  A  ; 
.  • .  A  is  B. 
The  minor  premiss,  when  stated  in  so  peculiar  a  form,  ot  course 
admits  of  simple  conversion,  and  thus  assumes  the  form  given  in  the 
text. 


76 


VARIOUS  KINDS  01  INFERENCES, 


X,  y,  z  are  B, 

The  individuals  (or  subordinate  species)  constituting 

the  group  A  are  x,  y,  z ; 
.*.  The  individuals  (or  subordinate  species)  constituting 

the  group  A  are  B. 

Such  an  inference  is  altogether  different  from  what  we 
now  understand  by  an  induction.  On  this  subject  the 
student  may  with  advantage  read  Mr.  Mill's  chapter  on 
'  Inductions  improperly  so  called/  See  Mill's  Logic, 
Bk.  III.  ch.  ii.  An  account  of  the  Aristotelian  induction 
will  be  found  in  Appendix  G  to  Dr.  Mansel's  edition  of 
Aldrich  ;  in  SirW.  Hamilton's -fiVj-^  on  Logic,  and  in  his 
Lectures  on  Logic,  Lect.  xvii.  and  Appendix  vii.  These 
authors,  as  already  noticed  in  the  case  of  Sir  W.  Hamil- 
ton, regard  inductions,  in  the  modern  sense  of  the  word, 
as  extra-logical.  The  advanced  student  may  also  consult 
with  advantage  Mr.  De  Morgan's  chapter  on  *  Induction,' 
Formal  Logic,  ch.  xi. 


CHAPTER   II. 
On  Immediate  Infere^ices. 

§  I.  AN  Immediate  Inference  may  be  formally  defined 
as  a  combination  of  two  propositions  of  which  one  is 
inferred  from  the  other,  the  proposition  inferred  being 
virtually  included  in  the  proposition  from  which  it  is 
inferred.  Of  Immediate  Inferences  the  most  important 
forms  are  Oppositions,  Conversions,  Permutations  ^ 

§  2.     On  Oppositions. 

Two  propositions  are  said  to  be  opposed  when  they 
have  the  same  subject  and  predicate,  but  differ  in  quan- 
tity or  quality  or  both.  An  Opposition  may  be  defined 
as  an  immediate  inference  in  which  from  the  truth 
or  falsity  of  one  proposition  we.  infer  either  the  truth 
or  falsity  of  another,  this  proposition  having  the  same 
subject  and  predicate  as  the  former,  but  differing  in 
quantity  or  quality  or  both.  Thus  from  the  propo- 
sition '  That  all  X  is  Y  is  true '  we  may  infer  the  pro- 
position '  That  no  X  is  Y  is  false,'  or  *  That  some  X 
is  Y  is  true,'  or  '  That  some  X  is  not  Y  is  false/ 

'  It  is  the  more  common  practice  to  speak  of  Opposition,  Con- 
version, and  Permutation,  but  I  have  adopted  the  plural  number  in 
order  to  draw  attention  to  the  fact  that  Logic  is  concerned  with  the 
results  rather  than  with  the  processes  by  which  they  are  arrived  at. 


78 


OPPOSITIONS, 


The  opposition  between 

A  and  E  is  called  a  Contrary  Opposition. 

I  and  O,  a  Subcontrary  Opposition. 

A  and  I,  or  E  and  O,  a  Subaltern  Opposition. 

A  and  O,  or  E  and  I,  a  Contradictory  Opposithan. 

These  forms  of  Opposition  are  exhibited  in  the  annexed 
scheme : — 


A 

• 

.     .  Contrary  .     . 

£ 

• 

• 
CO 

n 
•1 

S 

• 

• 

• 

V 

•                      • 

• 
C/5 

e 
cr 

9 

• 

• 

I    . 

.  Subcontrary  .    . 

• 

o 

If  A  be  true ;  E  is  false,  I  true,  O  false. 

If  A  be  false ;  E  is  unknown,  I  unknown,  O  true. 

If  E  be  true ;  A  is  false,  I  false,  O  true. 

If  E  be  false ;  A  is  unknown,  I  true,  O  unknown. 

If  I  be  true ;  A  is  unknown,  E  false,  O  unknown. 

If  I  be  false ;  A  is  false,  E  true,  O  true. 

If  O  be  true ;  A  is  false,  E  unknown,  I  unknown. 

If  O  be  false ;  A  is  true,  E  false,  I  true. 
It  will  be  observed  that  it  is  only  in  a  Contradictory 
Opposition  (where  the  opposed  terms  differ  both  in 
quantity  and  quality)  that  from  the  truth  or  falsity  of 
one  proposition  we  can  invariably  infer  the  truth  or 
falsity  of  another,  the  conclusion  which  we  draw  in  this 
case  being  from  the  truth  or  falsity  of  the  one  propo- 


OPPOSITIONS, 


79 


sition  to  the  falsity  or  truth  respectively  of  the  other. 
Hence  logicians  have  called  contradictory  the  most  per- 
fect form  of  opposition.  It  is  a  rule  of  practical  Logic 
that  a  contradictory  should  always  in  disputations  be 
used  in  preference  to  a  contrary  opposition ;  for  it  serves 
equally  well  the  purpose  of  contradicting  an  opponent, 
and  the  particular  proposition  which  it  asserts  affords 
less  ground  for  attack  than  an  universal.  Thus,  if  my 
opponent  asserts  A  (as  e.g.  All  philosophers  are  un- 
imaginative), I  may  meet  his  assertion  by  the  contra- 
dictory O  (Some  philosophers,  as  e.  g.  Plato,  Goethe,  &c., 
are  not  unimaginative),  and  from  this  position  I  cannot 
well  be  dislodged.  But  suppose  I  assert  in  opposition 
to  him  an  E  proposition  (No  philosophers  are  unima- 
ginative), he  will  probably  be  able  to  adduce  instances  of 
some  philosophers  who,  according  to  the  ordinary  mean- 
ing of  the  word  *  imaginative,'  would  be  called  unimagi- 
native, and  so,  by  meeting  my  E  with  an  I  proposition, 
gain  an  apparent  victory.  As  a  fact,  we  should  each  have 
made  assertions  too  wide,  but  he  would  have  succeeded  in 
dislodging  me  from  my  position,  whereas  (owing  to  my 
neglect  of  the  laws  of  contradiction)  I  should  not  have 
succeeded  in  dislodging  him  from  his. 


]^ote.—\\.  is  plain  that,  according  to  the  ordinary 
meaning  of  the  word  *  opposition,'  it  is  somewhat  of 
an  abuse  of  language  to  speak  ^ of  A  and  I,  or  E  and 
O  propositions  as  being  opposed.     It  would  be  better 


8o 


CONVERSIONS, 


if  this  form  of  inference  were  called  Subalternation  or 
Subordination. 

Nor,  strictly  speaking,  can  the  relation  between  I  and 
O  be  called  one  of  opposition,  for  they  may  both  be  true 
together.  Accordingly,  Aristotle  says  that  in  reality  (/car 
aKr]6eLav)  there  are  three  forms  of  opposition  (those  be- 
tween A  and  E,  A  and  O,  E  and  I),  though  in  language 
[Kara  rr)v  \e^Lv)  there  are  four  (adding  that  between  I  and 
O).     What  is  called  Subaltern  Opposition  he  does  not 


recognise. 

§  3.     On  Conversions. 

A  proposition  is  said  to  be  converted  when  its  terms  are 
transposed,  so  that  the  subject  becomes  the  predicate,  and 
the  predicate  the  subject.  A  Conversion  may  be  defined 
as  an  immediate  inference  in  which  from  one  proposition 
we  infer  another  having  the  same  terms  as  the  original 
proposition,  but  their  order  reversed.  This  inference  in 
some  cases  necessitates  a  change  of  quantity  in  passing 
from  one  proposition  to  the  other,  and  then  it  is  called 
a  Conversion  per  accidens ;  when  it  necessitates  no  such 
change,  it  is  called  a  Simple  Conversion  ^. 

I  and  E  may  both  be  converted  simply.  Thus,  from 
*  Some  X  is  Y,'  or  *  Some  poets  are  philosophers,'  I  may 
infer  *  Some  Y  is  X,'  or  '  Some  philosophers  are  poets.' 
From  *  No  X  is  Y,'  or  '  No  savages  are  trustworthy,'  I 
may  infer  '  No  Y  is  X,'  or  '  No  trustworthy  persons  are 
savages.* 

*  It  is  proposed  by  Sir  W?  Hamilton  to  call  the  original  proposi- 
tion the  '  Convertend,'  the  inferred  proposition  the  '  Converse.' 


CONVERSIONS, 


81 


A  can  only  be  converted  per  accidens.  For  though  it 
may  sometimes  happen  that  the  subject  and  predicate  of 
an  A  proposition  are  co-extensive,  and  therefore  conver- 
tible, this  circumstance  is  not  implied  in  the  form  of  the 
proposition,  and  it  is  with  what  is  implied  in  the  form  of 
the  proposition  that  we  are  alone  concerned.  Thus,  if  I 
assert  the  proposition  '  All  plane  triangles  are  three-sided 
rectilineal  figures,'  it  happens  in  this  pardcular  case  that  I 
am  justified,  without  any  change  of  quantity,  in  stating 
the  converse,  '  All  three-sided  rectilineal  figures  are  plane 
triangles.'  But  if  I  state  that  '  All  plane  triangles  are 
rectilineal  figures,'  I  am  only  justified  in  inferring  that 
*  Some  rectilineal  figures  are  plane  triangles.'  As,  there- 
fore, the  general  form  of  an  A  proposition  does  not 
imply  the  simple  convertibility  of  the  subject  and  predi- 
cate, I  am  only  justified  in  inferring  from  '  All  X  is  Y,' 
that '  Some  Y  is  X.' 

In  those  cases,  however,  in  which  the  form  of  the  pro- 
position implies  that  the  subject  .and  predicate  are  co- 
extensive, the  proposition,  though  an  A  proposition,  may 
be  converted  simply.  Thus,  from  the  proposidons  *  The 
second  legion  is  the  only  legion  quartered  in  Britain,' 
'Virtue  is  the  condition  of  Happiness,'  *A11  plane  tri- 
angles may  be  defined  as  three-sided  rectilineal  figures,' 
it  may  be  inferred  by  simple  conversion  that  '  The  only 
legion  quartered  in  Britain  is  the  second  legion,*  'The 
condition  of  Happiness  is  Virtue,'  '  All  three-sided  recti- 
lineal figures  may  be  called  plane  triangles.' 

An  O  proposition  cannot  be  converted  at  all.     From 

G 


82 


PERMUTA  TIONS, 


*  Some  X  is  not  Y,'  it  does  not  follow  that  '  Some  Y  is 
not  X,'  for  Y  may  stand  to  X  in  the  relation  of  a  species 
to  a  genus.  Thus  from  the  proposition  '  Some  Euro- 
peans are  not  Frenchmen/  I  cannot  infer  that  '  Some 
Frenchmen  are  not  Europeans.' 

§  4.     On  Permutations  ^ 

A  Permutation  may  be  defined  as  an  immediate  Infer- 
ence in  which  from  one  proposition  we  infer  another 
differing  in  quality,  and  having,  therefore,  instead  of  the 
original  predicate  its  contradictory.     Thus : — 

From  All  X  is  Y,  we  may  infer  that  No  X  is  not-Y. 

From  No  X  is  Y, All  X  is  not-Y. 

From  Some  X  is  Y, Some  X  is  not  not-Y. 

From  Some  X  is  not  Y,     .     .     .  Some  X  is  not-Y. 

The  legitimacy  of  these  inferences  is  apparent  from  the 
fact  that  contradictory  terms  (A  and  not-A)  admit  of  no 
medium,  so  that,  if  I  predicate  the  one  affirmatively,  I  may 
always  predicate  the  other  negatively,  and  vice  vers^. 

The  O  proposition,  when  permuted  from  *  Some  X  is 
not  Y,'  into  '  Some  X  is  not-Y,'  may  of  course  be  con- 
verted into  'Some  not-Y  is  X.'  This  combination  of 
permutation  and  conversion  is  improperly  described  by 
Whately  and  many  previous  logicians  as  a  single  inference, 
and  styled  '  Conversion  by  Contra-Position  or  Negation.' 

'  The  terai  Permutation  is  borrowed  from  Mr.  Karslake's  Aids  to 
Logic,  The  same  inference  is  sometimes  called  Infinitation,  from  the 
Nomen  Infinitum,  or,  more  properly,  Nomen  Indefinitum  (not-Y,  as 
the  contradictory  of  Y),  which  is  employed  as  the  predicate. 


PERMUTA  TIONS, 


83 


It  may  assist  the   student  if  I  add  some  further   in- 
stances of  permutations  : — 

All  men  are  fallible,  .*.  No  men  are  infallible. 
No  men  are  infallible,  .*.  All  men  are  fallible. 
Some   poets   are   reflective,  .*.  Some   poets   are   not 

unreflective. 
Some  poets  are  not  unreflective,  .*.  Some  poets  are 

reflective. 
All  poets  are  men  of  genius, .'.  (by  permutation)  No 

poets   are  not-men-of-genius ;  .*.  (by   conversion) 

No  not-men-of-genius  (=None  but  men  of  genius) 

are  poets. 


JSlote. — I  have  here  employed  an  expression  *  Con- 
tradictory Terms,'  which  in  most  works  on  Logic  is 
explained  in  the  first  part,  as  included  under  the  doctrine 
of  Opposition  of  Terms.  It  seemed,  however,  desirable 
to  introduce  there  only  those  distinctions  of  terms  which 
were  likely  to  be  frequently  required  in  the  sequel  of 
the  work.  I  may  here  state  that  '  Contradictory  Terms,' 
such  as  white  and  not-white,  lawful  and  un-lawful,  are 
terms  which  admit  of  no  medium,  i.e.  terms  which  are 
not  both  predicable  of  the  same  thing,  while  one  or  other 
of  them  must  be  predicable  of  it.  '  Contrary  Terms,'  like 
good  and  bad,  black  and  white,  are  terms  which  are  the 
most  opposed  under  the  same  genus;  they  cannot  both 
be  predicated  of  the  same  thing,  but  it  is  not  necessary 
that  one  or  other  of  them  should  be  predicable  of  it. 

G  2 


CHAPTER  III. 
On  Mediate  Inference  or  Syllogism, 

§  I.     The  Structure  of  the  Syllogism. 

A  SYLLOGISM  may  be  defined  as  a  combination  of 
two  propositions,  necessitating  a  third  in  virtue  of  their 
mutual  connexion;  or  as  an  inference  in  which  one 
proposition  is  inferred  from  two  others  conjointly,  the 
inferred  proposition  being  virtually  contained  in  the  pro- 
positions from  which  it  is  inferred.  This  is  obviously  a 
definition  of  a  legitimate  syllogism.  There  may  (as  will 
appear  below)  be  apparent  syllogisms,  which  do  not 
fulfil  the  conditions  of  this  definition.  We  may  take  as 
instances  of  syllogisms : — 

(i)     All  B  is  A, 
AllCisB; 
.-.All  C  is  A. 

(2)  All  sovereign  powers  are  invested  with  supreme 

authority  over  their  subjects, 
All  republics  are  sovereign  powers ; 
.•.All  republics  are  invested  with  supreme  authority 
over  their  subjects. 

(3)  No  rectilinear  figure  is  bounded  by  one  line, 
A  circle  is  bounded  by  one  line ; 

.'.A  circle  is  not  a  rectilinear  figure. 


STRUCTURE   OF  THE  SYLLOGISM, 


85 


•» 


") 


The  proposition  inferred  is  called  the  Conclusion,  the  pro- 
positions from  which  it  is  inferred  the  Premisses,  either 
of  them  singly  being  called  a  Premiss, 

As  the  conclusion  is  virtually  contained  in  the  pre- 
misses conjointly,  it  is  plain  that  the  two  terms  of  the 
conclusion  must  occur  in  the  premisses,  one  in  either. 
If  both  terms  occurred  in  the  same  premiss,  the  other 
premiss  would  be  entirely  alien  to  the  conclusion.  The 
remaining  term  of  each  premiss  must  be  the  same  ;  else 
there  would  be  nothing  in  common  between  the  two 
premisses,  and  the  conclusion  could  not  be  said  to  be 
inferred  from  the  two  conjointly.  This  third  term,  with 
which  the  two  terms  of  the  conclusion  may  ,be  regarded 
as  compared,  is  called  the  middle  term.  The  predicate 
of  the  conclusion  is  called  the  major  term^  and  the  subject 
the  minor  term ;  the  premiss,  in  which  the  major  and 
middle  terms  are  compared,  is  called  the  major  Premiss^ 
and  should  always  be  stated  first ;  that  in  which  the  minor 
and  middle  terms  are  compared  is  called  the  minor  premiss. 
Thus  in  a  syllogism,  formally  stated,  there  are  always 
three  propositions  including  three  terms,  the  premisses 
occurring  first  and  the  conclusion  last.  But  practically, 
in  reasoning,  we  frequently  state  the  conclusion  first, 
introducing  one  or  both  premisses  with  such  a  word  as 
*  for '  or  '  because,'  as  stating  our  reason  for  the  assertion. 
Thus  I  may  say  *  I  will  not  go  out  to-day,  for  it  is  raining,' 
or,  *  I  will  not  go  out  to-day,  for  it  is  raining,  and  the 
rain  may  give  me  a  cold.'  When  stated  in  this  form,  the 
conclusion  is  called  by  the  older  logicians  the  Problema 


86        MEDIATE  INFERENCE  OR  SYLLOGISM, 

or  QucBsiio,  being  regarded  as  a  question  to  which  the 
reason  or  reasons  assigned  furnish  the  answer.  It  will  also 
have  occurred  to  the  student  that,  as  a  fact,  we  usually 
state  only  one  premiss,  leaving  the  other  (which  may 
be  either  the  major  or  minor)  to  be  understood.  Thus, 
instead  of  stating  Syllogism  (2)  formally,  as  above,  I 
should  in  an  actual  discussion  say,  *  A  republic  is  invested 
with  supreme  authority  over  its  subjects,  for  every  so- 
vereign power  is  invested  with  such  authority,'  or,  *A 
republic  is,  &c.,  for  it  is  a  sovereign  power,'  or  briefly, 
*  A  republic  (being  a  sovereign  power)  is  invested,'  &c. ; 
or,  the  premiss  coming  first,  '  Inasmuch  as  every  so- 
vereign power  is  invested,  &c.,  I  maintain  a  republic  to  be 
invested  with  that  authority,'  or,  *  Inasmuch  as  a  republic 
is  a  sovereign  power,  it  is  invested  with,'  &c.^  Instead 
of  suppressing  one  of  the  premisses,  I  may,  for  brevity's 
sake,  suppress  the  conclusion.  Thus  I  may  say  '  Ever}^ 
sovereign  power  is  invested  with  supreme  authority  over 
its  subjects,  and  a  republic  is  a  sovereign  power,'  leaving 
it  to  the  hearer  or  reader  to  draw  the  conclusion  for  him- 
self. The  syllogism  does  not  pretend  to  be  the  form,  or 
even  a  form,  in  which  our  reasonings  are  usually  stated, 
but  simply  one  of  the  ultimate  analyses  of  them. 

As  every  term  in  the  syllogism  occurs  twice,  it  should 
be  noticed  that,  on  both  occasions,  it  should  be  used  in 
the  same  sense,  or,  to  adopt  technical   language,  every 

'  A  syllogism  with  a  suppressed  premiss  is  by  Aldrich  wrongly 
identified  with  the  Enthymeme  of  Aristotle.  Such  a  syllogism  was 
called  by  the  Stoics  a  avWoyiafibs  ixovoXrjiiiiaTos. 


STRUCTURE  OF  THE  SYLLOGISM, 


87 


.^r, 


term  in  the  syllogism  should  be  used  univocally.  If  we 
use  a  term  equivocally,  i.e.  in  two  entirely  different  senses, 
or  even  analogously,  i.e.  in  two  different  senses  having 
some  relation  to  each  other,  it  is  plain  that,  logically 
speaking,  we  are  using  two  different  terms,  and  con- 
sequently the  syllogism  will  include  four  terms  instead 
of  three.  This  caution  includes  the  rule  usually  given  by 
logicians  against  an  ambiguous  middle.  The  neglect  of  it, 
palpable  as  it  might  be  supposed  to  be,  is  often,  espe- 
cially in  a  long  course  of  reasoning,  very  difficult  of 
detection,  and  is  a  fertile  source  of  fallacy.  I  may  adduce 
as  very  simple  instances : — 

Humanity  is  a  moral  virtue, 
The  study  of  polite  letters  is  humanity ; 
.'.The  study  of  polite  letters  is  a  moral  virtue. 

The  church  is  the  aggregate  of  all  Christian  people. 
This  particular  congregation  (or  particular  building) 
is  the  church  (meaning  at  some  particular  place) ; 
.•.This  particular  congregation^ (or  particular  building) 
is  the  aggregate  of  all  Christian  people. 
In  the  former  case,  the  term  *  humanity '  has  come  to  be 
used  in  such  widely  different  senses,  that  it  may  be  re- 
garded as  used  equivocally;  in  the  latter  case,  the  senses 
of  the  word  *  church '  are  perhaps  sufficiently  nearly  allied 
to  be  regarded   as   analogous.     All   cases  of  what  are 
termed  '  Verbal  Fallacies '  may  be  referred  to  this  head. 


Note. — The  words  '  major,'  *  minor,'  and  '  middle,*  as 
applied  to  the  terms  in  a  syllogism,  have  been  inherited 


88 


MEDIATE  INFERENCE   OR  SYLLOGISM, 


by  all  subsequent  logicians  from  the  nomenclature  of 
Aristotle.  He  regarded  what  we  shall  presently  call  the 
First  Figure  (B  is  or  is  not  A,  C  is  B,  .*.  C  is  or  is 
not  A)  as  the  perfect  type  of  syllogism,  and,  amongst 
other  modes,  stated  it  in  the  form  C  is  in  B  (to  r  eoriV  eV 
oXo)  TO)  b),  B  is  or  is  not  in  A,  .*.  C  is  or  is  not  in  A, 
Thus  stated,  C  appears  to  be  the  smallest,  B  the  inter- 
mediate, and  A  the  largest  term  in  extent.  See  Prior 
Analytics,  Bk.  I.  ch.  iv.  In  negative  propositions,  however, 
we  have  no  means  of  determining  the  relative  extent  of 
the  subject  and  predicate,  and  consequently  Aristotle's 
nomenclature  does  not  properly  apply  to  negative  syl- 
logisms. To  affirmative  syllogisms  in  the  first  figure, 
whether  universal  or  particular,  it  applies  only  in  a 
modified  shape,  for  the  propositions  All  X  is  Y,  Some 
X  is  Y,  though  they  imply  that  Y  cannot  be  less  in 
logical  extent  than  All  X  in  the  one  case  or  than  Some  X 
in  the  other,  do  not  exclude  the  possibility  of  the  subject 
and  predicate  being  co-extensive.  Hence,  however  con- 
venient it  may  be,  Aristotle's  nomenclature  applies  only, 
and  that  not  with  strict  accuracy,  to  two  forms  of  syllo- 
gism (Barbara  and  Darii)  in  the  first  figure. 

§  2.     On  Moods  and  Figures, 

I  now  proceed  to  consider  the  possible,  not  the 
legitimate,  forms  of  syllogism.  Here  there  are  two  cir- 
cumstances to  be  taken  into  consideration:  ist,  that 
syllogisms  may  vary  according  to  the  quantity  and  quality 


MOODS  AND  FIGURES. 


89 


of  the  propositions  (A,  E,  I,  O)  of  which  they  are  com- 
posed ;  2nd,  that  they  may  vary  according  to  the  position 
of  the  terms  in  the  premisses.  The  first  consideration 
gives  us  the  number  of  possible  moods,  the  second  the 
number  of  possible  figures.  It  is  by  combining  these 
two  sources  of  variation  that  we  shall  obtain  the  number 
of  possible  syllogisms. 

There  are,  if  we  take  into  consideration  the  conclu- 
sion, sixty-four  possible  arrangements  of  the  propositions 
A,  E,  I,  O,  i.  e.  in  technical  language,  sixty-four  possible 
moods,  viz.  AAA,  AAE,  AAI,  AAO,  &c.  But  if  we  con- 
sider the  premisses  only,  the  number  of  possible  moods 
is  limited  to  sixteen,  viz.  AA,  AE,  AI,  AO,  EA,  EE, 
EI,  EO,  lA,  IE,  II,  10,  OA,  OE,  01,  00.  In  deter- 
mining what  possible  moods  are  legitimate,  we  may  either 
ask  '  Is  this  conclusion  justified  by  these  premisses  ?  * 
or  *  To  what  conclusion  do  these  premisses  lead  ? '  If  we 
ask  the  former  question,  we  must  examine  the  sixty-four 
possible  moods  in  which  the  conclusion  appears  as  well 
as  the  premisses ;  if  the  latter,  an  examination  of  the  six- 
teen possible  arrangements  of  premisses  is  sufficient. 

With  respect  to  the  possible  arrangements  of  the  terms 
in  the  premisses  (i.  e.  the  figures,  as  they  are  technically 
called)  there  are  also  two  methods  of  proceeding.  Taking 
no  account  of  the  conclusion  (and  therefore  not  knowing 
which  is  the  major  term  and  which  the  minor),  and 
asking  simply  '  In  how  many  ways  can  the  middle  term 
be  combined  with  the  other  terms  in  the  premisses?' 
there  are  three  possible  figures ;  viz.  ist,  that  in  which  the 


90        MEDIATE  INFERENCE  OR  SYLLOGISM. 

middle  term  is  subject  in  one  premiss  and  predicate  in 
the  other ;  2nd,  that  in  which  it  is  predicate  in  both  pre- 
misses ;  3rd,  that  in  which  it  is  subject  in  both.  But  if  we 
take  account  of  the  conclusion,  we  are  able  to  distinguish 
the  major  and  minor  terms,  and  consequently  the  major 
and  minor  premisses.  In  this  case,  there  are  four  possible 
figures,  viz.  ist,  that  in  which  the  middle  term  is  subject 
in  the  major  premiss  and  predicate  in  the  minor;  2nd, 
that  in  which  it  is  predicate  in  both  premisses ;  3rd,  that 
in  which  it  is  subject  in  both ;  4th,  that  in  which  it  is 
predicate  in  the  major  premiss  and  subject  in  the  minor. 
These  four  figures  may  be  exhibited  thus : — 


Fig.  I. 

Fig.  2. 

Fig.  3. 

Fig.  4. 

BA 

AB 

BA 

AB 

CB 

CB 

BC 

BC 

.-.CA 

.-.CA 

.-.CA 

.  * .  vx  A. 

If  we  take  no  account  of  the  conclusion,  either  extreme 
in  the  premisses  may  become  the  major  term,  and  the 
three  figures  may  be  represented  thus : — 

Fig.  I.  Fig.  2.  Fig.  3. 

BA  AB  BA 

CB  CB  BC 

/.CAorAC  .-.CAorAC  .-.CAorAC. 

§  3.  Determination  of  the  Legitimate  Moods  of  Syllogism, 

Note, — Few  difficulties  in  elementary  Logic  are  more 
likely  to  embarrass  the  beginner  than  the  variety  of 
methods  of  constituting  the  Legitimate  Moods  of  Syllo- 
gism.    Sir  W.  Hamilton,  as  a  consequence  of  quantifying 


LEGITIMATE  MOODS  OF  SYLLOGISM, 


91 


the  predicate,  is  able  to  represent  all  syllogisms  as  equa- 
tions, and  thus  to  exhibit  every  afiirmative  syllogism  as 
a  direct  application  of  what  is  called  the  Law  of  Identity 
(Every  A  is  A),  and  every  Negative  Syllogism  as  a  direct 
appHcation  of  the  Law  of  Contradiction  (No  A  is  not- A)  2. 
Besides  Sir  W.  Hamilton,  other  logicians  who  do  not, 
like  him,  quantify  the  predicate,  have  also  attempted 
to  enunciate  general  principles  equally  applicable  to 
all  syllogisms.  See  e.g.  Port  Royal  Logic,  Part  III. 
ch.  X.  Others  (as  Abp.  Thomson,  Laws  of  Thought, 
§  96,  and  Lambert,  as  quoted  by  Dr.  Mansel  in  his 
Notes  on  Aldrich^  ch.  iii.  §  6)  enunciate  a  distinct 
principle  for  each  figure.  Others  (and  pre-eminently 
Aristotle)  enunciate  a  canon  for  the  first  figure  ^,  and  test 

"^  These  two  Laws  (or  Principles)  together  with  the  Law  or  Principle 
of  Excluded  Middle  (A  either  is  or  is  not  B)  and  the  Law  or  Principle 
of  Sufficient  Reason  (Infer  nothing  without  a  ground  or  reason),  are 
often  called  the  Fundamental  Laws  of  Thought.  See  Thomson's 
Laivs  of  Thought ^  §  i  I4j  and  Hamilton's  Lectures  on  Logic ^  Lects.  vi. 
and  vii.  ^ 

*  lii'^oyiiv  h\  TO  KaTOi  -navros  Karriyopetadai,  orav  fir]d€v  y  Xa0€iv 
rS)v  Tov  vrroKfifxivov,  KaO*  oiv  Oartpov  ov  Xex^^^^'''^^'  ^^^  ^^  KaraL 
fjiTjSivos  wffavTcos,  An.  Pr.  I.  I ;  oaa  Kara  tov  fcaTrjyopovixtvov  \4y€TCU 
vdvTa  Kol  /caroL  tov  viroKuyLivov  /irjO-qafrai,  Cat.  3.  This  principle  or 
canon  in  its  Latin  form  was  called  by  the  Schoolmen  the  Dictum  de 
Omni  et  Nullo.  It  is  thus  stated  by  Sanderson  :  *  Dictum  de  Omni 
est  hujusmodi :  Quidquid  affirmatur  Universaliter  de  aliquo  Subjecto, 
affirmari  necesse  est  de  iis  quse  sub  eo  continentur.  Dictum  de  Nullo 
hujusmodi :  Quidquid  negatur  Universaliter  de  aliquo  Subjecto, 
negari  necesse  est  de  iis  quae  sub  eo  continentur.*  By  Aldrich  it  is 
stated  in  a  more  compressed  form,  as  follows :  '  Quod  prgedicatur 
Universaliter  de  alio  (i.e.  de  termino  distributo),  sive  affirmative, 
sive  negative,  prsedicatur  similiter  de  omnibus,  sub  eo  contentis.* 


93        MEDIATE  INFERENCE  OR   SYLLOGISM. 

the  validity  of  syllogisms  in  all  other  figures  by  reducing 
them  to  the  first.  Lastly,  a  favourite  method  amongst 
logicians  is  to  enumerate  the  faults  which  are  incident 
to  a  syllogism,  and  then  reject  those  moods  in  which 
they  are  found.  This  method  is  often  combined  with 
one  or  more  of  the  others.  Aldrich,  for  instance,  enun- 
ciates general  canons  of  syllogism,  then  uses  the  method 
I  have  last  explained,  and  finally  reduces  syllogisms  in 
the  other  figures  to  their  corresponding  forms  in  the  first. 


In  accordance  with  the  ordinary  practice  of  elementary 
treatises,  and  as  being  perhaps  at  first  more  intelligible 
to  the  learner,  I  shall  take  into  consideration  the  con- 
clusion, and  consequently  regard  the  number  of  figures  as 
four,  and  that  of  possible  moods  as  sixty-four,  reserving  for 
a  note  the  shorter  and  more  scientific  procedure.  The  pro- 
blem therefore  now  before  us  is  to  determine  which  of  the 
sixty-four  moods  are  admissible  in  each  of  the  four  figures. 

In  the  first  figure  our  task  is  easy.  There  we  are  able 
to  establish  a  canon  which  will  determine  directly  the 
legitimate  moods. 

With  a  little  attention  the  student  will  be  able  to  per- 
ceive the  truth  of  the  following  propositions : — 

(a)  If  one  term  be  affirmed  of  another  (provided  the 
latter  be  taken  in  its  entire  extent),  and  this  term 
of  a  third,  the  first  may  be  affirmed  of  the 
third. 

(^)  If  one  term  be    denied  of  another  (provided  the 


LEGITIMATE  MOODS  OF  SYLLOGISM. 


93 


latter  be  taken  in  its  entire  extent),  and  this  term 
affirmed  of  a  third,  the  first  may  be  denied  of 
the  third. 

(y)  If  one  term  be  affirmed  of  another  (even  though 
the  latter  be  taken  in  its  entire  extent),  and  this 
term  denied  of  a  third,  we  are  not  justified  in 
drawing  any  conclusion  as  to  the  relation  of  the 
first  to  the  third.  For,  if  one  term  be  denied  of 
another,  it  does  not  follow  that  whatever  may 
be  predicated  of  this  first  term  may  also  be 
denied  of  the  other :  thus  I  may  deny  *  red '  of 
*  blue,'  but  it  does  not  follow  that  '  colour,'  which 
I  predicate  of '  red,'  may  also  be  denied  of  '  blue.' 

(fi)  If  one  term  be  denied  of  another  (even  though 
the  latter  be  taken  in  its  entire  extent),  and  this 
term  denied  of  a  third,  no  conclusion  can  be 
drawn  as  to  the  relation  of  the  first  to  the  third. 
For,  because  I  deny  one  term  of  another,  it  does 
not  follow  that  whatever  I  can  deny  of  the 
first  can  also  be  denied  of  the  other,  nor  does 
it  follow  that  it  can  be  affirmed  of  it :  thus,  be- 
cause I  can  deny  '  white '  of  crows,  and  *  black ' 
of  *  white  '  (or  rather  of  the  corresponding  com- 
mon term  'white  things'),  it  does  not  follow 
that  I  can  deny  *  black '  of  crows ;  nor,  because 
I  can  deny  *  white '  of  crows  as  well  as  *  yellow ' 
of  '  white '  (or  *  white  things  %  does  it  follow  that 
I  can  affirm  *  yellow  '  of  crows. 
Putting  together  these  results,  we  obtain  the  following 


94       MEDIATE  INFERENCE  OR  SYLLOGISM. 

canon  of  reasoning  in  the  first  figure  :  If  one  term  can  be 
affirmed  or  denied  of  another  (provided  that  the  latter  be 
taken  in  its  entire  extent),  and  this  term  affirmed  of  a  third, 
the  first  can  be  affirmed  or  denied  (respectively)  of  the 
third ;  and,  if  these  conditions  are  not  fulfilled,  no  con- 
clusion can  be  drawn  *.  The  onlj  moods  which  fulfil  the 
conditions  of  the  canon  are  AAA,  EAE,  All,  and  EIO. 
The  conclusions  of  two  other  moods,  namely,  AAI  and 
EAO,  might  be  inferred^  by  Subaltern  Opposition,  from 
those'  of  AAA   and  EAE,  and  hence   these   are  called 

Subaltern  Moods, 

We  have  obtained,  it  will  be  observed,  forms  of  syl- 
logism capable  of  proving  any  one  of  the  four  propo- 
sitions, A,  E,  I,  or  O,  and  into  one  or  other  of  the  types 
accepted  as  legitimate  moods  of  the  first  figure  all  our 
mediate  reasonings  may  be  thrown.  Here,  then,  our 
enquiry  might  terminate,  if  it  were  simply  our  object  to 
obtain  a  sufficient  number  of  legitimate  types  of  reason- 
ing, but  the  problem  before  us  is  to  state  exhaustively  all 
possible  forms  which  can  be  accepted  as  legitimate. 

There  being  no  canon  which  distinguishes  with  equal 
precision  the  legitimate  and  illegitimate  moods  of  the 
other  figures,  we  must,  in  discussing  them,  have  recourse 
to  some  other  method.  I  shall  first  enumerate  and  ex- 
plain certain  syllogistic  rules  (derived  from  the  definition 

*  It  will  be  plain  from  the  statement  of  the  Canon  that  the  major 
premiss  of  a  syllogism  in  the  first  figure  must  be  universal.  At  the 
suggestion  of  Mr.  St.  G.  Stock  of  Pembroke  College,  this  fact  has 
been  made  plainer  in  the  statement  of  the  Canon  itself  than  was  the 
case  in  the  earlier  editions. 


SYLLOGISTIC  RULES, 


95 


of  a  syllogism)  which  will  exclude  illegitimate  moods, 
and  then,  before  accepting  the  remainder,  I  shall  test 
them  by  reducing  them  to  the  first  figure. 


Syllogistic  Rules, 

I.  The  middle  term  must  he  distributed  at  least  once.  For, 
if  in  both  premisses  it  were  used  in  only  a  partial  signifi- 
cation, it  might  denote  entirely  different  objects  in  the 
one  premiss  from  those  which  it  denoted  in  the  other, 
and  so  there  might  be  no  connexion  between  the  two 
premisses.  Thus,  in  the  premisses  '  All  men  are  animals,' 
'  All  horses  are  animals,'  the  part  of  the  group  '  animals  ' 
which  is  coincident  with  'men'  may  be,  and  here  is, 
entirely  distinct  from  that  portion  of  the  group  which 
is  coincident  with  '  horses,'  and  consequently  we  can 
draw  no  conclusion  as  to  the  relation  betw^een  men  and 
horses.     This  fallacy  is  called  Undistributed  Middle, 

II.  If  a  term  be  distributed  in  the  conclusion,  it  must  have 
been  previously  distributed  in  the  premisses.  The  reason  is 
obvious.  If  we  use  a  term  in  a  partial  signification  in 
the  premisses,  we  cannot  legitimately  use  it  in  its  entire 
signification  in  the  conclusion.  To  do  so  would  be  to 
argue  from  part  to  whole,  or,  in  other  words,  to  employ 
a  term  in  a  wider  signification  in  the  conclusion  than 
that  in  which  it  is  employed  in  the  premisses. 

This  fallacy  is  called  illicit  process  of  the  major  or  minor, 
according  as  the  term  illegitimately  distributed  in  the  con- 
clusion is  the  major  or  minor  term.     In  the  syllogism. 


St  I 


I 
^1 


g6       MEDIATE  INFERENCE  OR  SYLLOGISM, 

Some  A  is  not  B, 
All  B  is  C, 
.*.  Some  C  is  not  A, 

we  have  illicit  process  of  the  major ;  in  the  syllogism, 

All  B  is  A, 
Some  C  is  B, 
.-.  All  C      A, 

illicit  process  of  the  minor. 

III.  Two  negative  premisses  prffve  nothing.  For  they 
simply  assert  that  there  is  no  connexion  between  the 
middle  term  and  the  extremes;  consequently  we  can 
draw  no  conclusion  with  respect  to  the  relation  of  the 
extremes. 

IV.  1/  either  of  the  premisses  be  negative,  the  conclusion 
must  be  negative.  For  the  other  premiss  is  affirmative, 
and,  if  in  one  premiss  we  affirm  a  connexion  between 
the  middle  term  and  one  of  the  extremes,  and  in  the 
other  premiss  deny  any  connexion  between  the  middle 
term  and  the  other  extreme,  there  can  be  no  connexion 
between  the  two  extremes. 

V.  If  the  conclusion  be  negative,  one  of  the  premisses  must 
he  negative.  For  we  cannot  deny  tha  there  is  any  con- 
nexion between  the  extremes,  except  we  have  previously 
denied  that  there  is  any  connexion  between  one  of  the 
extremes  and  the  middle  term. 

VI.  Two  particular  premisses  prove  nothing.     For  they ' 
cannot  be  both  negative  (O,  O).     Nor  can  they  be  both 
affirmative  (I,  I),  for  then  the  middle  term  would  be  undis- 


SYLLOGISTIC  RULES. 


97 


tributed.  The  only  remaining  case  is  that  of  one  affirma- 
tive and  one  negative  premiss  (I,  O).  But  this  combina- 
tion of  premisses  would  leave  no  term  to  be  distributed  in 
the  conclusion.  Hence  the  conclusion  would  be  an  I  pro- 
position, an  affirmative  conclusion  inferred  from  a  negative 
premiss,  which  (according  to  Rule  IV)  is  illegitimate. 

VII.  If  one  premiss  be  particular,  the  conclusion  must  be 

particular. 

« 

The  premisses  must  be  either  both  affirmative,  or  one 
affirmative  and  one  negative  (see  Rule  III). 

Now,  if  they  are  both  affirmative,  they  will  (by  Rule  VI) 
be  A  and  I.  This  combination  of  premisses,  as  it  contains 
only  one  distributed  term,  and  the  middle  term  must  be 
distributed  at  least  once  (Rule  I),  leaves  no  term  to  be 
distributed  in  the  conclusion :  consequently  the  conclusion 
must  be  I. 

If  the  premisses  are  one  affirmative  and  one  negative, 
they  must  (by  Rule  VI)  be  either  O  and  A  or  I  and  E.  In 
either  case  the  premisses  distribute  only  two  terms,  and, 
as  one  of  them  must  be  the  middle  term  (by  Rule  I),  there 
remains  only  one  term  to  be  distributed  in  the  conclusion. 
But  the  conclusion  must  be  negative  (by  Rule  IV).  There- 
fore, it  must  be  O  ^ 

The  converse  of  this  Rule,  viz.  that  a  particular  con- 
clusion necessitates  a  particular  premiss,  is  not  true. 
The  only  cases  however  in  which  we  find  a  particular 

^  This  proof  is  substituted  for  the  somewhat  more  elaborate  proof 
given  in  the  earlier  editions. 

H 


98        MEDIATE  INFERENCE   OR   SYLLOGISM, 

conclusion  without  a  particular  premiss  are  those  in 
which  the  premisses  assume  more  than  is  required  in 
order  to  prove  the  conclusion.  This  fact  will  be  apparent 
to  the  student  from  an  examination  of  the  individual 
cases,  and  it  might  be  laid  down  as  a  rule  that,  wherever 
there  is  a  particular  conclusion  without  a  particular  pre- 
miss, something  superfluous  is  invariably  assumed  in  the 
premisses  ®. 

Of  the  above  Rules,  it  is  plain  that  Rules  III,  IV,  V, 
VI,  VII  are  applicable  to  the  moods  before  they  are  re- 
ferred to  the  several  figures,  Rules  I  and  II  are  applicable 
only  when  the  moods  are  referred  to  some  particular 
figure. 

By  the  application  of  the  first  set  of  Rules,  the  sixty- 
four  possible  moods  are  reduced  to  twelve,  viz. 
AAA,  AAI,  AEE,  AEO,  All,  AOO, 
EAE,  EAO,  EIO,  lAI,  IEO^  OAO. 
Thus  EEE  is  rejected  because  it  has  two  negative  pre- 
misses, EAA  because  it  has  a  negative  premiss  without 
a  negative  conclusion,  AAE  because  it  has  a  negative 

•  The  syllogistic  rules  are  comprised  in  the  mnemonic  lines : — 

Distribuas  medium ;  nee  quartus  terminus  adsit. 

Utraque  nee  prsemissa  negans,  nee  particularis. 

SectetUr  partem  conclusio  deteriorem. 

Et  non  distribuat,  nisi  cum  prsemissa,  negetve. 
'  It  has  been  suggested  to  me  by  Professor  Park  that  lEO  might 
be  rejected  by  the  application  of  Rule  II,  even  before  it  is  referred  to 
any  particular  figure.  For  the  conclusion,  O,  distributes  its  predicate, 
that  is  the  major  term  of  the  syllogism.  But  the  major  premiss, 
being  I,  evidently  does  not  distribute  this  term.  Consequently,  there 
is  invariably  Illicit  Process  of  the  Major. 


SYLLOGISTIC  RULES, 


\ 


99 


conclusion  without  a  negative  premiss,  III  because  it  has 
two  particular  premisses,  lAA  because  it  has  a  particular 
premiss  without  a  particular  conclusion. 

By  the  application  of  Rules  I  and  II  to  these  twelve 
moods,  when  referred  to  the  several  figures,  there 
remain : — 

in  fig.  2,  EAE,    AEE,    EIO,    AOO,    EAO,    AEO; 
in  fig.  3,  AAI,     EAO,    lAI,     OAO,    All,       EIO; 
in  fig.  4,  AAI,     AEE,     lAI,     EAO,    EIO,      AEO. 

I  append  a  few  examples  of  the  methgd  of  testing  the 
moods,  when  referred  to  the  figures. 

Take  AEE  in  figure  2. 

A    ^       All  A  is  B, 

E  No  C  is  B  ; 

E       .  • .  No  C  is  A.    No  fault. 

Take  lEO  in  figure  3. 

I  Some  B  is  A, 

E  No  B  is  C ; 

0  .  • .  Some  C  is  not  A. 

Illicit  process  of  major. 

Take  All  in  figure  4. 

A  All  A  is  B, 

1  Some  B  is  C ; 

I       .  • .  Some  C  is  A.     Undistributed  middle. 

It  will  be  seen  that  of  the  sixty-four  moods,  when  re- 
ferred to  the  four  figures,  there  are  only  six  in  each  which 
have  not  been  rejected.     It  now  remains  further  to  test 

H  2 


I 


lOO      MEDIATE  INFERENCE   OR  SYLLOGISM, 

these  moods  in  the  second,  third,  and  fourth  figures  by 
reducing  them  to  moods  in  the  first. 


Reduction. 

As  we  have  adopted  no  canon  for  the  second,  third,  and 
fourth  figures,  we  have  as  yet  no  positive  proof  that  the  six 
moods  remaining  in  each  of  those  figures  are  valid ;  we 
merely  know  that  they  do  not  offend  against  any  of  the 
syllogistic  rules.  But,  if  we  can  reduce  them,  i.  e.  bring 
them  back  to  the  first  figure,  by  shewing  that  they  are 
only  different  statements  of  its  moods,  or,  in  other  words, 
that  precisely  the  same  conclusions  can  be  obtained  from 
equivalent  premisses  in  the  first  figure,  their  validity  will 
be  proved  beyond  question.  There  are  two  methods  of 
performing  this  operation:  ist,  that  called  Osiensive  Re- 
duction, which  consists  in  employing  one  or  more  of 
the  processes  of  conversion,  permutation,  and  trans- 
position of  premisses;  2nd,  that  called  Reductio  per  im- 
possibile,  which  consists  in  shewing,  by  means  of  the  first 
figure  and  the  laws  of  opposition,  that  the  contradictory 
of  the  conclusion  is  false,  and  therefore  the  conclusion 
itself  true.  Either  of  these  methods  is  applicable  to  all 
the  eighteen  moods,  and  the  result  is  that  all  are  proved 
to  be  valid.  I  shall  give  instances  of  the  application  of 
each  method. 

By  ostensive  reduction  I  shall  test  EAO  in  the 
fourth,  lAI  in  the  third,  AEE  and  AOO  in  the  second 
figures. 


REDUCTION                    ^              lOI 

Fig.  4. 

Fig.  I. 

E 

No  A  is  B. 

.  • .  No  B  is  A.  (Simple  Conversion.) 

A 

All  B  is  C. 

.  • .  Some  C  is  B.  (Conversion  per  ace.) 

0. 

• .  Some  C  is  not  A. 

Some  C  is  not  A. 

Fig.  3. 

Fig.  I. 

I 

Some  B  is  A.  ->..^,^ 

^^         All  B  is  C. 

A 

All  B  is  C.      ^ 

*^^  .  • .  Some  A  is  B.  (Simple  Conversion.) 

I.- 

.  €ome  C  is  A. 

Some  A  is  C. 
.  • .  Some  C  is  A.  (Simple  Conversion.) 

Fig.  2. 

Fig.  I. 

A 

All  A  is  B.     -^.^^^ 

^^    .  • .  No  B  is  C.  (Simple  Conversion.) 

E 

No  C  is  B.      -^^ 

"^        All  A  is  B. 

E. 

• .  No  C  is  A. 

No  A  is  C. 
.  • .  No  C  is  A.  (Simple  Conversion.) 

Fig.  2. 

Fig.  I. 

A 

All  A  is  B. 

.  • .  No  A  is  not-B.  (Permutation.) 
.  • .  No  not-B  is  A.  (Simple  Conversion.) 

0 

Some  C  is  not  B. 

.  • .  Some  C  is  not-B.  (Permutation.) 

0. 

• .  Some  C  is  not  A. 

Some  C  is  not  A. 

The  mark  x  shews  that  the  premisses  are  transposed ; 
the  sign  .  * .  on  the  right-hand  side  of  the  page  is  here 
appropriated  to  express  the  employment  of  conversion  or 
permutation.  The  last  example  is  interesting,  because 
AOO  in  fig.  2,  and  OAO  in  fig.  3,  inasmuch  as  they 
contain  O  premisses,  cannot  be  reduced  by  the  ordinary 
methods  of  transposition  of  premisses  and  conversion. 
Hence  the  older  logicians  (who,  with  few  exceptions,  did 
not  recognise  permutation)  applied  to  them  the  tedious 
method  of  reductio  per  inipossibile  (or,  if  we  write  it  in  full, 
reductio  per  deduciionem  ad  impossibtle).  This  method  is 
equally  applicable  to  all  the  imperfect  moods,  as  the  moods 
of  the  three  last  figures  are  often  called.     I  now  proceed 


, 


I0!2     MEDIATE  INFERENCE  OR  SYLLOGISM. 

to  give  an  example  of  it,  and  shall  select  AAI  in  the 
third  figure. 

A  All  B  is  A, 

A  All  B  is  C ; 

I         .  • .  Some  C  is  A. 

This  conclusion  must  be  true :  for,  if  not,  suppose 
it  to  be  fal^e ; 

Then  its  contradictory  must  be  true,  i.  e. 

No  C  is  A.  \ 

But  (from  the  premisses)  All  B  is  C.       >  Syll.  II. 
.  • .  (By  figure  i )  No  B  is  A.  ) 

But  (from  the  premisses)  All  B  is  A. 

Now  these  two  (being  contrary  propositions)  cannot 

both  be  true. 
But  the  proposition  All  B  is  A  is  assumed  to  be  true. 
.  • .  The  proposition  No  B  is  A  must  be  false. 

Hence,  either  the  reasoning  of  Syll.  II.  is  faulty,  or 

one  of  the  premisses  is  untrue. 
But  the  reasoning  (being  in  the  first  figure)  must  be 

valid. 

.  • .  One  of  the  premisses  is  false. 

Now  the  premiss  '  All  B  is  C,'  being  one  of  the  pre- 
misses of  the  original  syllogism,  is  assumed  to  be 
true. 

.  • .  The  other  premiss  (No  C  is  A)  must  be  false. 
.  • .  Its  contradictory  (Some  C  is  A)  is  true. 


REDUCTION. 


103 


As  the  positive  test  of  reduction  confirms  in  every  case 
the  negative  test  of  the  syllogistic  rules,  it  follows  that  six 
moods  (though  not  the  same  six  moods)  are  valid  in  each 
figure.  These  moods  may  be  remembered  by  means  of 
the  mnemonic  lines : — 

Barbara,  Celarent,  Darii,  Ferioo^t,  prioris  : 
Cesar e,  Camestres,  Festtno,  Baroko,  secundse : 
Tertia,  Darapti,  Disamis,  Daiisi,  Felapton, 
Bokardo,  Ferison,  habet :  Quarta  insuper  addit 
Bramantip,  Camenes,  Dimarts,  Fesapo,  Fresison  : 
Quinque  Subalierni  totidem  Generalibus  orti, 
Nomen  habent  nullum,  nee,  si  bene  colligis,  usum. 

In  the  above  lines,  the  initial  consonants,  B,  C,  D,  F, 
shew  that  the  mood  in  the  second,  third,  or  fourth  figure 
to  which  they  are  prefixed  is  to  be  reduced  to  the  mood 
correspondingly  marked  in  the  first.  Thus  Disamis,  when 
reduced,  will  become  Darii.  The  vowels  shew  the 
moods ;  thus  Disamis  represents  lAI  in  the  third  figure. 
The  letter  j,  when  it  occurs  after  a  vowel,  shews  that  the 
proposition  for  which  that  vowel  stands  is  to  be  converted 
simply,  the  letter  p  that  it  is  to  be  converted  per  accidens  ^ 

*  It  should  be  noticed  that  when  these  letters  follow  the  conclusion, 
as  is  the  case  in  Camestres,  Disamis,  Bramantip^  Camenes,  Dimaris, 
they  apply  not  to  the  conclusion  of  the  mood  given  for  reduction 
but  to  the  conclusion  of  the  equivalent  mood  in  the  first  figure,  to 
which  such  mood  is  to  be  reduced.  Thus,  in  reducing  Bramantip, 
the  student  will  find  that  the  /  affects  not  the  I  conclusion  of 
Bramantip,  but  the  A  conclusion  of  the  corresponding  syllogism  in 
Barbara.     See,  for  other  instances,  p.  loi. 


I04      MEDIATE  INFERENCE   OR  SYLLOGISM, 

The  letter  m  shews  that  the  premisses  are  to  be  trans- 
posed, k  that  the  mood  is  to  be  reduced  per  impossibile. 
It  will  be  noticed  that  k  occurs  only  in  two  moods, 
Baroko  and  Bokardo,  but  I  have  shewn  that  the  per 
impossibile  method  is  equally  applicable  to  all  imperfect 
moods,  and  that  these  two  moods  can  be  reduced  osten- 
sively  by  means  of  permutation,  so  that  any  imperfect 
mood  may  be  reduced  either  ostensively  or  per  impos- 
sibile K  The  initial  B  in  Baroko  and  Bokardo  shews  that 
the  per  impossibile  method,  in  their  case,  assumes  the 
validity  of  Barbara,  but  in  other  cases  the  operation 
may  assume  the  validity  of  some  one  of  the  other  moods 
in  the  first  figure;  thus,  in  the  particular  instance  I 
have  taken  above,  it  is  performed  by  means  of  Celarent. 
It  is  perhaps  needless  to  add  that  all  letters,  not  already 
explained  in  the  mnemonic  lines,  are  non- significant. 

The  nature  of  the  subaltern  moods  has  already  been 
explained.  They  are,  AAI,  EAO  in  fig.  i,  EAO,  AEO  in 
fig.  2,  and  AEO  in  fig.  4,  included  respectively  in  AAA, 
EAE,  EAE,  AEE,  AEE.  They  cannot  properly  be  re- 
garded as  illegitimate,  inasmuch  as  the  conclusions  are 
valid,  but  they  are  superfluous,  inasmuch  as  they  infer 
less  than  is  justified  by  the  premisses. 

*  If  we  take  k  to  signify  the  employment  of  permutation,  Baroko 
and  Bokardo  may  be  replaced  respectively  by  Fa/cso/f o  and  Do«samosit. 
These  terms  are  adapted  from  Whately's  Logic,  Bk.  II.  ch.  iii.  §  5. 


(  ' 


SPECIAL  RULES. 


The  special  Rules, 


105 


Besides  the  general  syllogistic  rules,  already  enunciated 
and  proved,  certain  Special  Rules  have  been  enunciated 
for  each  figure.  I  give  them  below  as  generally  stated. 
Those  for  the  first  figure  have  been  proved  in  establishing 
its  canon;  those  for  the  other  figures  the  student  may 
verify  for  himself  by  applying  the  rules,  already  laid 
down,  on  the  distribution  of  terms. 

Fig.  I.  (a)  The  minor  premiss  must  be  affirmative. 

(^)  The  major  premiss  must  be  universal. 
Fig.  2.  (a)  One  or  other  premiss  must  be  negative. 

(p)  The  conclusion  must  be  negative. 

(7)  The  major  premiss  must  be  universal. 

Fig-  3-  («)  The  minor  premiss  must  be  affirmative. 
{0)  The  conclusion  must  be  particular. 

Fig.  4.  (a)  When  the  major  premiss  is  affirmative,  the 
minor  must  be  universal. 

{0)  When  the  minor  premiss  is  affirmative,  the 
conclusion  must  be  particular. 

(y)  In  negative  moods  the  major  premiss  must 
be  universal. 

(S)  The  conclusion  cannot  be  an  universal  affir- 
mative, nor  either  of  the  premisses  a  par- 
ticular negative. 


/ 


I06      MEDIATE  INFERENCE   OR  SYLLOGISM, 

Note, — If,  leaving  out  of  consideration  the  conclusion, 
we  regard  the  number  of  possible  figures  as  three  and 
that  of  possible  moods  as  sixteen,  we  may  proceed  as 
follows. 

Having  enunciated  the  canon  of  the  first  figure,  we 
may  constitute  the  moods  Barbara^  Celarent,  Darn,  and 
Ferio.  The  subaltern  moods,  AAI  and  EAO,  are  not 
admissible,  as  the  question  here  before  us  is  not  '  What 
conclusions  are  justified  by  such  and  such  premisses,' 
but  '  To  what  conclusions  do  such  and  such  premisses 
lead  ? '  Now,  from  this  point  of  view,  the  conclusions 
of  the  subaltern  moods  are  not  directly  inferred  from 
the  premisses,  but  are  inferred  by  subalternation  from 
the  universal  conclusions  to  which  the  premisses  directly 
lead.  The  same  observation  will  of  course  apply  to  the 
subaltern  moods  in  the  other  figures. 

If  we  take  no  account  of  the  conclusion,  we  have 
no  means  of  determining  which  is  the  major  and  which 
is  the  minor  term.  Consequently,  the  premisses  may 
lead  to  two  kinds  of  conclusions :  ist,  those  in  which 
the  predicate  of  the  first  premiss  is  predicated  of  the 
subject  of  the  second ;  2nd,  those  in  which  the  subject 
of  the  second  premiss  is  predicated  of  the  predicate  of 
the  first.  Now  the  canon  of  the  first  figure  applies  only 
to  the  fir^st  case;  consequently  we  are  bound  to  ask  if 
any  conclusions,  falling  under  the  second  head,  may  be 
inferred  from  the  premisses.  These  cannot  be  deter- 
mined directly  by  the  canon,  but  must  be  determined  in 
the  same  manner  as  conclusions  in  the  second  and  third 


/ 


INDIRECT  MOODS, 


107 


figures.  Here  we  proceed  by  a  method  similar  to  that 
employed  in  the  text.  The  syllogistic  rules  exclude  seven 
of  the  sixteen  possible  moods,  viz.  EE,  EO,  OE,  00,  II, 
10,  01.  When  the  moods  are  referred  to  their  several 
figures,  we  find  that,  where  the  extreme  employed  in  the 
first  premiss  becomes  the  predicate,  and  the  extreme 
employed  in  the  second  premiss  the  subject  of  the  con- 
clusion, the  results  are,  in  the  second  figure,  Cesare,  Ca- 
mesires,  Fesiino,  Baroko ;  in  the  third,  Darapti,  Disamis, 
Datm\  Felaplon,  Bokardo,  Feruon,  the  subaltern  moods 
of  the  second  figure  EAO,  AEO,  being  inadmissible. 
Where  the  extreme  employed  in  the  first  premiss 
becomes  the  subject,  and  the  extreme  employed  in 
the  second  premiss  the  predicate  of  the  conclusion, 
the  results  are,  in  the  first  figure,  AAI,  AEO,  All, 
EAE,  lEO,  which,  when  we  transpose  the  premisses, 
become  respectively  Bramantip,  Fesapo,  Dimaris,  Camenes, 
and  Fresison  in  the  fourth  figure.  Hence,  according 
to  this  mode  of  treatment,  the  moods  of  the  fourth 
figure  are  regarded  as  indirect  moods  of  the  first. 
Similarly,  in  the  second  figure  we  may  constitute  the 
indirect  moods  AEE,  EAE,^  lEO,  OAO.  These,  if  we 
transpose  the  premisses,  are  merely  a  repetition  of  the 
ordinary  moods  of  the  second  figure.  This  is  also  the 
case  with  the  indirect  moods  of  the  third  figure,  viz.  AAI, 
AEO,  All,  AOO,  lAI,  lEO.  It  will  therefore  be  seen 
that,  with  the  exception  of  rejecting  the  subaltern  moods, 
which  even  there  we  regarded  as  superfluous,  we  arrive 
practically  at  the  same  results  as  in  the  text.     The  moods 


108      MEDIATE  INFERENCE   OR  SYLLOGISM, 

of  the  fourth  figure  are  recognised,  but,  instead  of  being 
regarded  as  moods  of  a  distinct  figure,  they  are  treated  as 
indirect  moods  of  the  first.  By  the  expression  *  indirect 
moods/  it  will  be  seen,  we  mean  moods  in  which  the 
extreme  employed  in  the  first  premiss  becomes  the  sub- 
ject, and  the  extreme  employed  in  the  second  premiss  the 
predicate  of  the  conclusion. 


/' 


— -s-^^^^J^H^^^""- 


CHAPTER  IV. 
On   Trains  of  Reasoning,    {The  Soi^ites) 

SYLLOGISMS  may  be  combined  in  what  is  called 
a  Train  of  Reasoning .  Thus  the  major  and  minor  pre- 
misses, or  either,  of  our  ultimate  syllogisms  may  them- 
selves be  proved  by  syllogisms;  the  major  and  minor 
premisses  of  these,  or  either,  by  other  syllogisms,  and 
so  on,  till  at  last  we  come  to  premisses  not  admitting 
of  syllogistic  proof.  Such  premisses  are  either  assumed 
without  any  proof  at  all,  or  they  are  the  result  either  of 
direct  observation  or  of  the  testimony  of  others  or  of 
Induction. 

In  a  train  of  reasoning,  any  syllogism  proving  a  pre- 
miss of  a  subsequent  syllogism  is  called  with  reference 
to  the  subsequent  syllogism  a  Pro-Syllogism,  and  the 
subsequent  syllogism  with  reference  to  it  an  Epi-Syllo- 
gism.  It  is  obvious  that  the  very  same  syllogism  in 
different  relations  may  be  called  a  Pro- Syllogism  or  an 
Epi- Syllogism.  '«' 

The  Sorites  (or,  as  it  is  sometimes  called,  the  chain- 
argument)  is  a  common  instance  of  a  train  of  reasoning 
in  a  compressed  form.  It  consists,  in  its  proper  and 
most  usual  form,  of  a  series  of  propositions,  in  which 
the  predicate  of  the  preceding  is  always  the  subject  of 
the  succeeding  premiss.  The  conclusion  predicates  the 
last  predicate  of  the  first  subject. 


110 


TRAINS  OF  REASONING, 


THE  SORITES. 


Ill 


Thus,— All  A  is  B, 

All  B  is  C, 

All  C  is  D, 

All  D  is  E ; 

.  • .  All  A  is  E. 

When  expanded,  the  Sorites  contains  as  many  syllo- 
gisms as  there  are  propositions  intermediate  between  the 
first  proposition  and  the  conclusion.  These  syllogisms 
are  in  the  first  figure,  and  the  conclusion  of  each  becomes 
the  minor  premiss  of  the  next.  Thus,  the  above  Sorites 
contains  three  syllogisms,  viz. — 

(i)  All  B  is  C, 

All  A  is  B ; 

.  • .  All  A  is  C. 

(2)  All  C  is  D, 
All  A  is  C ; 

.  • .  All  A  is  D. 

(3)  All  D  is  E, 
All  A  is  D; 

.  • .  All  A  is  E. 

In  a  Sorites,  only  one  premiss  can  be  particular,  viz. 
the  first ;  and  only  one  negative,  viz.  the  last  \ 

*  The  first  premiss,  if  particular,  may  be  stated  in  the  form  *  Some 
B  is  A,'  instead  of  in  the  usual  form  *  Some  A  is  B' ;  the  first  syllogism 
of  the  expanded  Sorites  will  then  be  in  the  third  figure  instead  of  the 
first.  Similarly,  the  last  premiss,  if  negative,  may  be  stated  in  the 
form  *  No  E  is  D,'  instead  of  in  the  form  '  No  D  is  E,*  which  will 


/■ 


For,  if  there  were  a  particular  premiss  in  any  place 
except  the  first,  there  would  be  a  particular  major,  which, 
in  the  first  figure,  is  inadmissible. 

Again,  if  any  premiss  except  the  last  were  negative, 
there  would  be  a  negative  conclusion  in  one  of  the  pre- 
vious syllogisms ;  this  conclusion  would  necessitate,  in  the 
following  syllogisms,  a  negative  minor,  which,  in  the  first 
figure,  is  inadmissible. 


IVofe. — Besides  the  above  form  of  Sorites,  there  is 
another  called  the  Regressive  or  Goclenian  Sorites  (so 
called  from  Goclenius,  who  first  noticed  it).  Its  pro- 
perties are  exactly  the  reverse  of  those  of  the  ordinary 
Sorites.  The  subject  of  each  premiss  becomes  the  pre- 
dicate of  the  next,  the  conclusion  predicates  the  first 
predicate  of  the  last  subject,  the  conclusion  of  each  of 
the  expanded  syllogisms  becomes  the  major  premiss  of 
the  next,  and  the  rules  by  which  it  is  governed  are  that 
the  first  premiss  only  can  be  negative  and  the  last  par- 
ticular.    It  may  be  stated  thus : — 

All  E  js  F, 
All  D  is  E, 
All  C  is  D, 
All  B  is  C, 
All  A  is  B  ; 
.-.All  A  is  F. 

make  the  last  syllogism  of  the  expanded  Sorites  a  syllogism  of  the 
second  figure.  No  advantage,  however,  is  gained  by  this  mode  of 
statement,  and  it  is  not  nearly  so  simple  as  the  usual  form. 


CHAPTER  V. 

On  Complex  {Hypothetical)  Propositions  and 

Syllogisms. 

HITHERTO  I  have  treated  only  of  simple  (or,  as 
they  have  been  inaccurately  termed,  Categorical)  pro- 
positions and  syllogisms.  A  Complex  (or,  as  it  is  com- 
monly called,  a  Hypothetical)  Syllogism  is  one  in  which 
one  or  more  complex  (or  hypothetical)  propositions 
occur.  A  complex  proposition  is  a  combination  of  two 
or  more  simple  propositions  in  one  sentence,  the  pro- 
positions being  so  related  that  the  truth  or  falsity  of  one 
proposition  or  set  of  propositions  is  made  to  depend  on 
the  truth  or  falsity  of  the  other  proposition  or  set  of 
propositions.  If  the  two  propositions  or  sets  of  propo- 
sitions be  associated  together,  so  that  the  truth  of  one 
depends  on  the  truth  of  the  other,  the  complex  propo- 
sition may  be  called  Conjunctive\     If  they  be  dissociated, 

1  The  word  categorical  {Karri-^opiKos)  properly  means  affirmative, 
and  IS  always  used  in  that  sense  by  Aristotle. 

''  I  have,  in  accordance  with  more  ancient  usage,  employed  the 
word  *  conjunctive '  in  place  of  the  word  *  conditional,'  which  is 
employed  by  Aldrich  and  other  logicians  of  his  time.  Instead  of 
simple  and  complex  propositions,  they  speak  of  categorical  and 
hypothetical,  subdividing  hypothetical  into  conditional  and  disjunc- 
tive.     Besides  the  improper  use  of  the  word  categorical  (noticed 


COMPLEX  PROPOSITIONS  AND  SYLLOGISMS,    II3 

SO  that  the  truth  of  one  depends  on  the  falsity  of  the 
other,  and  the  falsity  of  one  on  the  tryth  of  the  other, 
the  complex  proposition  may  be  called  Disjunctive.  Thus 
we  may  take  as  instances  of  Conjunctive  Propositions  : — 

If  (or  When,  Where,  Provided  that,  &c.)  A  is  B,  C  is  D  ; 
If  A  is  not  B,  C  is  D;  If  A  is  not  B,  C  is  not  D ;  If  A  is 
B  and  C  is  D,  E  is  F;  If  A  is  B,  either  C  is  D  or  E  is  F 
or  G  is  H ;  If  either  A  is  B  or  C  is  D,  E  is  F. 

It  will  be  noticed  in  the  second  and  third  examples 
that  negatives  are  introduced,  but  they  are,  notwith- 
standing, examples  of  conjunctive  propositions,  for  C 
being  D  in  the  first  case,  and  C  not  being  D  in  the 
second,  are  made  to  depend  on  the  truth  of  A  not 
being  B.  As  instances  of  Disjunctive  Propositions  we 
may  take  the  following : — 

Either  A  is  B,  or  C  is  D ;  Either  A  is  B,  or  C  is  D,  or 
E  is  F ;  A  is  either  B  or  C  or  D ;  Either  A  or  B  or  C  is 
D ;  Either  A  is  not  B,  or  C  is  not  D ;  Either  A  is  B,  or 
C  is  not  D. 

This  form  of  proposition  implies  that  the  truth  of  one 
member  involves  the  falsity  of  the  other,  and,  vice  versa, 
the  falsity  of  one  member  the  truth  of  the  other. 

It  should  be  noticed  that  both  conjunctive  and  dis- 
junctive propositions  admit  of  being  reduced  to  the 
simple  form.     Thus  : — 

above),  it  is  extremely  awkward  to  make  hypothetical  and  conditional 
(which  are  synonyms)  stand  respectively  for  the  genus  and  species. 
The  words  conjunctive  and  disjunctive  serve  also  to  point  out  that  the 
division  of  complex  propositions  is  exhaustive. 

I 


114   COMPLEX  PROPOSITIONS  AND  SYLLOGISMS, 


*  If  A  is  B,  C  is  D '  becomes  '  The  case  of  A  being  B 
is  a  case  of  C  being  D '  or  *  A  being  B  involves  as  a  con- 
sequence C  being  D/ 

The  disjunctive  proposition,  when  analysed,  contains 
four  conjunctive  propositions,  each  of  which  may  be 
reduced  to  a  simple  proposition.  Thus,  *  Either  A  is  B, 
or  C  is  D'  is  equivalent  to  the  four  conjunctive  pro- 
positions :  If  A  is  B,  C  is  not  D ;  If  A  is  not  B,  C  is  D ; 
If  C  is  D,  A  is  not  B ;  If  C  is  not  D,  A  is  B.  Of  these 
four  propositions,  however,  the  third  is  implied  in  the  first, 
and  the  fourth  in  the  second. 

I  now  proceed  to  consider  Complex  Syllogisms,  i.e. 
syllogisms  which  contain  Complex  Propositions. 

J  2.  I.    Conjunctive  Syllogisms, 

A  Conjunctive  Syllogism  is  a  syllogism,  one  or  both 
of  whose  premisses  are  conjunctive  propositions;  if  only 
one  premiss  be  conjunctive,  the  other  must  be  simple. 
If  both  premisses  be  conjunctive,  inasmuch  as  all  con- 
junctive propositions  rank  as  universal  affirmatives,  the 
syllogism,  to  be  valid,  must  be  conformed  to  Barbara  in 
the  first  figure.     Thus, 

IfAisB,  CisD, 
•     If  C  is  D,  E  is  F ; 
.  • .  If  A  is  B,  E  is  F, 
is  a  vallid  syllogism ;  but  the  following  would  not  be  valid : 

If  A  is  B,  C  is  D, 
If  AisB,  EisF; 
.-.IfCisD,  EisF. 


CONJUNCTIVE  SYLLOGISMS, 


115 


Far  the  most  common  form  however  of  a  conjunctive 
syllogism  is  that  in  which  the  major  is  a  conjunctive, 
and  the  minor  a  simple  proposition.  Of  this  form  there 
are  four  possible  varieties,  of  which  two  are  valid  and 
two  invalid.     These  may  be  represented  thus : — 

If  A  is  B,  C  is  D.     (Major  premiss.) 


(i)     AisB; 

.  • .  C  is  D. 
(a)     A  is  not  B ; 

No  conclusion. 


0)    CisD; 

No  conclusion. 
(2)     CisnotD; 
.  • .  A  is  not  B. 


Hence  we  obtain  the  rule  that,  if  we  affirm  the  antece- 
dent, we  must  affirm  the  consequent,  or,  if  we  deny  the 
consequent,  we  must  deny  the  antecedent ;  but,  if  we  deny 
the  antecedent  or  affirm  the  consequent,  no  conclusion 
can  be  drawn.  The  reason  of  this  rule  will  be  obvious 
on  a  little  reflexion.  We  assert  that  *  A  being  B  involves 
as  a  consequence  C  being  D ' ;  hence,  if  we  grant  that  A 
is  B,  it  must  follow  that  C  is  D ;  if  we  deny  that  C  is  D, 
it  must  follow  that  what  involves  it  as  a  consequence 
must  also  be  untrue ;  but  C  might  still  be  D,  though  A 
were  not  B,  nor  would  it  follow  from  C  being  D  that  A 
was  also  B. 

Syllogism    (i)    is    called    a    Constructive   conjunctive 
syllogism. 

Syllogism    (2)    is    called    a    Destructive    conjunctive 
syllogism. 

It  may  be  useful  to  add  a   few  examples  of  valid 
conjunctive  syllogisms.  x 

I  2 


Il5   COMPLEX  PROPOSITIONS  AND  SYLLOGISMS. 

(i)    If  A  is  B,  C  is  not  D. 

C  is  D  ; 
.  • .  A  is  not  B. 

(2)  If  A  is  not  B,  CisD. 

A  is  not  B  ; 
.  • .  C  is  D. 

(3)  If  A  is  not  B,  C  is  not  D. 


A  is  not  B  ; 
.  • .  C  is  not  D. 


C  is  not  D ; 
•.  A  is  B. 

CisD; 
.  A  is  B. 


(4)  If  A  is  B,  either  C  is  D  or  F  is  G. 


AisB; 

.-.Either  C  is  D  or  F  is  G. 


Neither  C  is  D  nor  F  is  G ; 
.  • .  A  is  not  B. 


(5)  If  either  C  is  D  or  F  is  G,  either  X  is  Y  or  V  is  W. 


Either  C  is  D  or  F  is  G  ; 


NeitherXisYnorVisW; 


•.Either  XisYor  Vis  W.    .'.  Neither  C  is  D  nor  F  is  G. 


#3.  II.    Disjunctive  Syllogisms. 

A  Disjunctive  Syllogism  is  a  syllogism  of  which  the 
major  premiss  is  a  disjunctive,  and  the  minor  a  simple 
proposition,  the  latter  affirming  or  denying  one  of  the 
alternatives  stated  in  the  former. 

We  may  indeed  combine  two  disjunctive  propositions, 
and  draw  conclusions  from  them,  but  we  can  only  do  so 
after  reducing  the  disjunctive  propositions  to  the  con- 
junctive form.    Thus  from  the  two  propositions  Either 


DISJUNCTIVE  SYLLOGISMS, 


117 


A  is  B  or  C  is  D,  Either  A  is  B  or  E  is  F,  we  may  draw 
four  conclusions,  viz.  If  C  is  D,  E  is  F ;  If  C  is  not  D,  E  is 
not  F;  If  E  is  F,  C  is  D ;  If  E  is  not  F,  C  is  not  D.  But, 
as  these  conclusions  are  really  drawn  from  conjunctive 
propositions  which  are  involved  in  the  two  disjunctive 
propositions,  we  are  not  justified  in  calling  the  syllogisms 
disjunctive.  Hence,  as  will  be  noticed,  my  definition  of 
disjunctive  is  not  so  wide  as  that  of  conjunctive  syllo- 


gisms. 


The  disjunctive  syllogism  admits  of  four  conclusions, 
which  may  be  exhibited  thus : — 


Either  A  is  B,  or  C  is  D. 


(I) 
(2) 


AisB; 
.'.C  is  not  D. 

A  is  not  B ; 
.-.CisD. 


(3)         CisD; 
.',  A  is  not  B. 
-  (4)         Cisnot  D; 
.'.AisB. 


I  add  a  few  examples : — 

Either  A  is  B,  or  C  is  not  D. 

(i)        AisB;  j      1(3)        CisnotD; 

.-.CisD. 
(2)         A  is  not  B;  (4) 

.  • .  C  is  not  D. 

Either  A  is  B,  or  C  is  D,  or  E  is  F. 
(i)  A  is  B  j  .-.  Neither  C  is  D  nor  E  is  F. 

(2)  A  is  not  B ;  .-.  Either  C  is  D  or  E  is  F. 

(3)  Neither  C  is  D  nor  E  is  F;  .-.A  is  B. 


.  * .  A  is  not  B. 

CisD. 
.-.A  is  B. 


Il8    COMPLEX  PROPOSITIONS  AND  SYLLOGISMS, 


(4)  Either  C  is  D  or  E  is  F;  .-.A  is  not  B. 

(5)  Either  A  is  B  or  C  is  D ;  .-.E  is  not  F. 

&c.  &c. 

He  is  either  a  fool  or  a  knave. 


(i)     He  is  a  fool; 

.  • .  He  is  not  a  knave. 
(2)     He  is  a  knave; 

.'.He  is  not  a  fool. 


(3)  He  is  not  a  fool ; 
.  • .  He  is  a  knave. 

(4)  He  is  not  a  knave ; 
.'.He  is  a  fool. 


iVb/^.— Mr.  Mill  (in  his  Examination  of  Sir  W.  HamiU 
ion's  Philosophy,  ch.  xxiii.)  maintains  that  a  disjunctive 
proposition  merely  implies  that  the  two  alternatives  cannot 
both  be  false,  but  that  it  does  not  exclude  the  possibility 
of  both  of  them  being  true.  Thus,  in  the  last  example, 
he  would  maintain  that  there  is  nothing  in  the  form  of 
the  assertion  to  exclude  the  supposition  of  the  man  being 
both  a  fool  and  a  knave.  In  this  opinion  he  is  preceded 
by  many  other  logicians,  but  it  seems  to  me  that  in  the 

expression  'either or '  we  distinctly  exclude  the 

possibility  of  both  alternatives  being  true,  as  well  as  of 
both  being  false.  In  fact,  when  we  do  not  wish  to  ex- 
clude the  possibility  of  both  being  true,  we  add  the  words 
*  or  both,'  thus :  '  He  is  either  a  fool  or  a  knave,  or  both'; 
'  I  shall  come  either  to-day  or  to-morrow,  or  perhaps  both 
days.' 


THE  DILEMMA, 


119 


\  4.     The  Dilemma, 

There  remains  the  case  in  which  one  premiss  of  the 
complex  syllogism  is  a  conjunctive  and  the  other  a  dis- 
junctive proposition,  it  being,  of  course,  understood  that 
the  disjunctive  proposition  deals  only  with  expressions 
which  have  already  occurred  in  the  conjunctive  pro- 
position. This  form  is  called  a  Dilemma,  The  order  of 
the  premisses  is  different,  but  it  seems  more  natural  that 
the  conjunctive  proposition  should  be  the  major.  If  we 
consider  the  case  in  which  the  major  consists  of  one 
antecedent  and  several  consequents,  there  is  only  one 
valid  form  of  argument,  and  that  is  destructive. 

(i)    If  A  is  B,  CisDandEisF; 

But  either  C  is  not  D  or  E  is  not  F ; 
.•.A  is  not  B. 

If  we  asserted  in  the  minor  *  C  is  D  and  E  is  F '  there 
would  be  no  conclusion,  and  if  we  asserted  *  Neither  C  is 
D  nor  E  is  F,'  the  minor  would  not  be  disjunctive.  The 
assertion  *  Either  C  is  D  or  E  is  F '  is,  according  to  my 
view  of  the  significance  of  a  disjunctive  proposition, 
equivalent  to  the  assertion  '  Either  C  is  not  D  or  E  is  not 
F,'  and  leads  to  the  same  conclusion. 

If  the  major  consist  of  several  antecedents,  and  one 
consequent,  there  is  only  one  valid  form  of  argument, 
and  that  is  constructive. 

(2)    If  AisBorifEisF,  CisD; 
But  either  A  is  B  or  E  is  F ; 
.-.C  is  D. 


I20    COMPLEX  PROPOSITIONS  AND  SYLLOGISMS, 

If  we  asserted  in  the  minor  *  C  is  not  D/  it  would  not 
satisfy  the  requirements  of  the  definition  by  being  a  dis- 
junctive proposition. 

In  the  remaining  case,  where  there  are  several  ante- 
cedents and  several  consequents,  there  are  two  valid 
forms,  one  constructive  and  the  other  destructive. 

{3)     If  A  is  B,  C  is  D  ;  and  if  E  is  F,  G  is  H; 
But  either  A  is  B,  or  E  is  F ; 
.-.Either  C  is  D,  or  G  is  H. 

(4)    If  A  is  B,  C  is  D;  and  if  E  is  F,  G  is  H: 
But  either  C  is  not  D,  or  G  is  not  H  ; 
.-.  Either  A  is  not  B,  or  E  is  not  F. 

It  is  evident  that  we  may  form  a  Trilemma,  Tetra- 
lemma,  &c.,  by  increasing  the  number  of  antecedents 
or  consequents  or  both,  thus: — 

If  A  is  B,  or  if  E  is  F,  or  if  G  is  H,  C  is  D; 
But  either  A  is  B,  or  E  is  F,  or  G  is  H  ; 
.•.C  is  D. 

If  A  is  B,  C  is  D;  and  if  E  is  F,  G  is  H;  and  if 

I  is  J,  K  is  L  ; 
But  either  A  is  B,  or  E  is  F,  or  I  is  J; 
.-.  Either  C  is  D,  or  G  is  H,  or  K  is  L. 

It  is  not  uncommon  to  mistake  for  dilemma  what 
is  really  only  a  conjunctive  syllogism.  Thus  the  two 
following  syllogisms,  when  examined,  will  be  found 
to  be,  the  first  a  constructive,  the  second  a  destructive 
conjunctive. 


THE  DILEMMA. 


lai 


(i)  Whether  geometry  be  regarded  as  a  mental  dis- 
cipline  or  as    a   practical    science,  it  deserves 
to  be  studied; 
But  geometry  may  be  regarded  as  both  a  mental 
discipline  and  a  practical  science ; 
.'.It  deserves  to  be  studied. 

(2)  If  we  go  to  war,  we  must  either  contract  a  debt, 
or  increase  the  taxation,  or  indemnify  ourselves 
at  the  enemy's  expense ; 
We  shall  not  be  able  to  do  any  of  these ; 
.-.We  are  not  able  to  go  to  war. 

In  disputation,  the  adversary  who  is  refuted  by  a 
dilemma  is  said  to  be  '  fixed  on  the  horns  of  a  dilemma '; 
he  is  said  to  rebut  the  dilemma,  if  he  meet  it  by  another 
with  an  opposite  conclusion.  Thus  (to  tell  an  old  story) 
Protagoras  the  Sophist  is  said  to  have  engaged  with  his 
pupil,  Euathlus,  that  half  the  fee  for  instruction  should  be 
paid  down  at  once,  and  the  other  half  remain  due  till 
Euathlus  should  win  his  first  cause.  Euathlus  deferred 
his  appearance  as  ah  advocate,  till  Protagoras  became 
impatient  and  brought  him  into  court.  The  Sophist  then 
addressed  his  pupil  as  follows :  '  Most  foolish  young 
man,  whatever  be  the  decision,  you  must  pay  your 
money;  if  the  judges  decide  in  my  favour,  I  gain  my  fee 
by  the  decision  of  the  court,  if  in  yours  by  our  bargain/ 
This  dilemma  Euathlus  rebutted  by  the  following :  '  Most 
sapient  master,  whatever  be  the  decision,  you  must  lose 
your  fee ;  if  the  judges  decide  in  my  favour,  you  lose  it 


122    COMPLEX  PROPOSITIONS  AND  SYLLOGISMS, 

by  the  decision  of  the  court ;  if  in  yours,  by  our  bargain, 
for  I  shall  not  have  gained  my  cause.* 


THE  DILEMMA, 


123 


Note  I. — Of  the  four  cases  of  dilemma  which  I  have 
given,  the  first  would  not  be  admitted  by  Abp.  Whately 
and  Dr.  Mansel,  who  define  dilemma  as  'A  syllogism 
having  a  conditional  (i.  e.  conjunctive)  major  premiss  with 
more  than  one  antecedent,  and  a  disjunctive  minor.' 
Having  however  a  disjunctive  minor,  it  cannot  properly 
be  regarded  as  a  conjunctive  syllogism,  and  it  seems  less 
arbitrary  and  more  systematic  to  define  dilemma  as  'a 
syllogism  of  which  one  premiss  is  a  conjunctive  and  the 
other  a  disjunctive  proposition  *  than  to  limit  it  as  above. 

Note  2. — Few  parts  of  Logic  have  occasioned  more 
differences  of  opinion  or  nomenclature  than  the  theory 
of  complex  (or  hypothetical)  propositions  and  syllogisms. 
Sir  W.  Hamilton  (see  his  Lectures  on  Logic,  Lecture  xiii. 
and  Appendix  viii.)  finally  arrives  at  the  opinion  that 
*  hypothetical  and  disjunctive  judgments  *  are  not  more 
complex  than  ordinary  propositions,  and  that  '  hypo- 
thetical and  disjunctive  reasonings'  are  really  forms  of 
immediate  inference.  Thus  he  would  represent  the  con- 
junctive syllogism  in  the  form : — 

If  A  is  B,  C  is  D  ; 
.  • .  A  being  B,  C  is  D. 

The  disjunctive  syllogism  he  would  represent  in  the 
form : — 

Either  A  is  B,  or  C  is  D  ; 

.  • .  A  not  being  B,  C  is  D. 


The  other  inferences  from  the  premisses  would,  of 
course,  be  drawn  similarly.  % 

The  dilemma  would  assume  the  form : — 

If  A  is  B,  C  is  D;  and  if  E  is  F,  G  is  H; 
.  • .  Either  A  being  B,  or  E  being  F,  it  follows  that 
C  is  D,  or  G  is  H ; 
or    .  • .  Either  C  not  being  D,  or  G  not  being  H,  it  follows 
that  either  A  is  not  B,  or  E  is  not  F. 

Without  attempting  to  discuss  the  arguments  that  have 
been  adduced  on  either  side,  I  may  express  my  own 
opinion  that  complex  (or  hypothetical)  propositions  and 
syllogisms  are  rightly  so  called,  and  that  the  latter  are  to 
be  regarded  as  mediate,  and  not  as  immediate,  forms 
of  inference.  Though  no  new  term  is  introduced  in 
the  minor  premiss,  the  major  and  minor  premisses  are 
entirely  distinct  propositions,  and  the  conclusion  is  the 
result  not  of  one  proposition  but  of  two  propositions 
taken  conjointly. 


»<'^bJ^Sr^«e«^3i=:*:>» 


CHAPTER  VI. 


On  the  words  'Most',  'Many'  &c.,  as  express- 
ing the  Quantity  of  Propositions. 

TO  all  particular  propositions  I  have  hitherto  prefixed 
the  word  '  some/  Both  in  conversation  and  reasoning, 
however,  it  frequently  happens  that  we  use  some  other 
sign  of  particularity,  such  as  '  many,' '  most,'  &c.  Nor  does 
there  seem  any  valid  reason  why  these  forms  should  not 
be  recognised  by  Logic.  From  what  has  already  been  said 
of  particular  premisses,  it  will  be  seen  that  wherever  one 
premiss  is  universal  and  the  other  modified  by  some  sign 
of  particularity,  as  '  some,'  '  many,'  '  most,'  &c.,  the  con- 
clusion must  be  particular,  the  degree  of  particularity  in 
no  case  transcending  (though,  in  some  cases,  it  may  fall 
below)  that  denoted  by  the  particular  premiss.  Thus,  if 
we  state  as  our  premisses  '  All  crimes  are  to  be  punished,' 
*  Many  offences  against  individual  persons  are  crimes,'  we 
must  draw  the  conclusion  that  '  Many  offences  against 
individual  persons  are  to  be  punished.'  But  if  we  state 
as  our  premisses  '  All  crimes  are  to  be  punished,'  '  Most 
crimes  are  offences  against  individuals,'  we  are  only  justi- 
fied in  drawing  the  conclusion  that '  Some  offences  against 


'most'  'MANYI  £TC, 


125 


individuals  are  to  be  punished.'  The  student  will,  from 
the  principles  already  laid  down,  be  easily  able  to  dis- 
tinguish between  the  two  classes  of  cases. 

*  Two  particular  premisses  prove  nothing.'     This  is  a 
general  rule,  and  is  strictly  true  where  the  premisses  are 

quantified  as  *some' '  some.'    But  there  is  one  case 

in  which  two  particular  premisses  necessitate  a  conclu- 
sion. I  will  begin  with  a  simple  instance  of  it.  If 
two  different  predicates  can  both  be  predicated  affirma- 
tively of  the  greater  number  of  individuals  denoted  by 
the  same  common  term,  there  must  be  some  individuals 
of  which  they  can  both  be  predicated,  i.  e.  in  certain 
cases  the  predicates  must  be  predicable  of  each  other. 
Thus,  from  the  premisses 

Most  A  are  B, 
Most  A  are  C, 
we  must  necessarily  infer  that  Some  A  is  both  B  and  C, 
and  consequently  that  Some  B  are  C  and  Some  C  are  B. 

But  we  may  draw  the  same  conclusion,  even  in  those 
cases  in  which  both  premisses  are  not  quantified  by  the 
word  *  most,'  provided  that  the  sum  of  the  quantities  by 
which  the  subjects  are  affected  Exceeds  unity.      Thus 
from  the  premisses 

Three-fourths  of  A  are  B, 
One-third  of  A  is  C, 
it  follows  that  at  least  one-twelfth  of  A  is  both  B  and  C ; 
but  if  B  and  C  be  both  predicable  of  the  same  objects, 
either  must  be,  partially,  predicable  of  the  other.     If,  for 
instance,  three  men  out  of  four  exceed  a  certain  height 


125      'MOST'  'MANY'   ETC,   AS  EXPRESSING 


THE   QUANTITY  OF  PROPOSITIONS. 


127 


and  one  out  of  three  a  certain  weight,  at  least  one  out  of 
twelve  must  exceed  both  the  given  height  and  the  given 
weight,  and  we  may  affirm  both  that  Some  men  who 
exceed  a  certain  height  also  exceed  a  certain  weight,  and 
that  Some  men  who  exceed  a  certain  weight  also  exceed 
a  certain  height. 

Of  course,  when  we  use  such  an  indefinite  word  as 
*  most '  in  either  premiss,  the  other  premiss  must  be 
quantified  by  an  expression  signifying  at  least  one-half; 
else  we  cannot  be  sure  that  the  quantities  of  the  two 
premisses,  when  added  together,  exceed  unity. 

A  conclusion  of  this  kind  can  only  be  drawn  where 
the  subject  in  both  premisses  is  the  same  term,  i.e.  in 
the  third  figure ;  for,  in  the  mere  form  of  a  logical  pro- 
position, we  have  no  data  to  guide  us  with  regard  to  the 
quantity  of  the  predicate.     Thus,  from  the  premisses 
Nineteen-twentieths  of  A  are  B, 
Nine-tenths  of  B  are  C, 
we  can  draw  no  conclusion  as  to  the  relation  of  A  and  C ; 
for  the  tenth  of  B  which  is  not  C  might  be  precisely  that 
portion  which  was   coincident  with,  or  which  contained, 
the  nineteen-twentieths  of  A.     Though,    however,  these 
syllogisms  are  confined  to  the  third  figure,  they  may  be 
either  affirmative  or  negative.     Thus,  from  the  premisses 
Three-fourths  of  A  are  not  B, 
Two-thirds  of  A  are  C, 
we  may  infer  that  five-twelfths  at  least  of  A  are  C  and 
not  B,  and  consequently  that  some  "C  is  not  B,  and  some 
things  which  are  not  B  are  C. 


Note, — The  propositions  employed  in  the  above  chapter 
have  usually  been  regarded  as  Particulars,  though  they 
have  sometimes  been  classed  with  Universals.  See  Sir 
W.  Hamilton's  Lectures  on  Logic,  vol.  ii.,  first  ed.  p.  354 ; 
second  ed.  p.  361. 


j^ 


CHAPTER  VII. 


On  Probable  Reasoning. 

IN  discussing  the  copula,  it  was  maintained  that  any 
modification  of  our  assertions,  such  as  the  qualifications 
introduced  by  the  words  *  probably,'  *  possibly,'  &c.,  was, 
in  the  ultimate  analysis  of  the  proposition,  to  be  referred 
to  the  predicate  and  not  to  the  copula.  Thus  such  a 
proposition  as  *  A  is  probably  B,'  when  stated  in  its 
strictly  logical  form,  would  become  *  That  A  is  B  is  a 
probability/  It  would  however  be  tedious  and  prac- 
tically useless  to  reduce  all  our  propositions  to  such  a 
form.  I  may  therefore  proceed  to  lay  down  rules  for 
reasoning  from  propositions  whose  copula  is  modified, 
remembering  however  that  they  are  not  stated  in  strictly 
logical  language. 

The  correctness  of  the  following  rule  will  be  apparent. 
If  a  premiss  whose  copula  is  modified  be  combined  with 
another  premiss  whose  copula  is  unmodified,  the  copula 
of  the  conclusion  must  be  modified  also ;  the  modality,  of 
course,  never  transcending  that  of  the  premiss.  Thus 
from  the  premisses  *  All  true  poets  are  men  of  genius/ 
'  Sophocles  is  probably  (certainly,  possibly,  &c.)  a  true 
poet,'  I  infer  that  Sophocles  is  probably  (certainly,  pos- 
sibly, &c.)  a   man  of  genius.      From  a  certain  and  a 


PROBABLE  REASONING, 


129 


probable  premiss,  therefore,  arranged  according  to  the 
ordinary  laws  of  syllogism,  we  can  never  infqf  more  than 
a  probable  conclusion.  To  this  head  may  most  con- 
veniently be  referred  those  syllogisms  in  which  the  major 
is  a  particular  proposition  introduced  by  the  word  '  most,' 
and  the  minor  a  singular  proposition.  Thus  from  the  pre- 
misses, *  Most  philosophers  are  men  of  vivid  imagination,' 
*  A  B  is  a  philosopher,'  I  infer,  as  the  conclusion,  A  B 
is  probably  a  man  of  vivid  imagination.  If  most  phi- 
losophers possess  certain  characteristics,  any  particular 
philosopher  will  probably  possess  them,  so  that  the  major 
premiss  is,  in  fact,  equivalent  to  the  proposition,  *  A 
philosopher  is  probably  a  man  of  vivid  imagination.' 

Using  the  word  *  probable '  in  the  sense  of  '  more 
likely  than  not,'  two  probable  premisses  do  not  lead  to  a 
probable  conclusion.  This  fact  will  be  obvious  from  an 
easy  example.  Suppose  there  are  in  a  bag  four  red,  five 
blue,  and  six  white  balls :  I  may  say  with  truth  *  Any  ball 
drawn  at  random  from  the  bag  is  probably  a  red  or 
blue  ball ' ;  I  may  also  say  with  truth  '  Any  ball  drawn 
at  random  from  the  red  and  blue  balls  is  probably  a  blue 
ball';  but  I  cannot  infer  that  *  Anyl)all  drawn  at  random 
from  the  bag  is  probably  a  blue  ball.'  I  shall  only  be 
justified  in  drawing  the  conclusion  *Any  ball  drawn  at 
random  from  the  bag  is  possibly  a  blue  ball.'  But, 
where  our  information  is  so  special  as  in  the  above 
instance,  a  conclusion  of  this  kind  is  far  too  vague.  Is 
there  no  method  which  will  enable  me  to  state  in  the 
conclusion  the  exact  value  of  the  expectation  that  any 


I30 


PROBABLE  REASONI]\rG, 


particular  ball  drawn  at  random  may  be  blue,  red,  or  white  ? 
For  such  a  method  I  must  have  recourse  to  mathematics. 
Though  the  word  *  probable '  is  used  in  the  sense  of 
'  more  likely  than  not,'  the  word  prohahility  is  used  as 
the  equivalent  of  '  chance '  or  '  expectation/  If  it  be  three 
to  two  that  a  certain  event  will  happen,  3  :  2  is  called 
the  odds  for,  2:3  the  odds  against  the  event.  Now  the 
'  probability '  or  *  chance  *  of  the  event  happening  would 
be  expressed  by  |,  that  of  its  not  happening  by  f ,  the 
denominator  in  both  cases  being  expressed  by  the  sum  of 
the  terms  of  the  odds,  the  numerator  in  the  first  case  by 
the  term  of  the  odds  for,  in  the  latter  case  by  the  term 
of  the  odds  against.  If  two  events  are  independent  of 
each  other,  the  joint  or  compound  probability  that  they 
will  both  happen  must  be  much  smaller  than  the  pro- 
bability that  either  of  them  will  happen  alone,  and  it  is 
discovered  by  multiplying  together  the  fractions  which 
express  the  probabilities  of  their  happening  separately  ^ 
Thus,  in  the  above  instance,  the  chance  of  my  drawing 
a  red  or  blue  ball  =  y\ ;  the  chance  of  my  drawing  out 
of  the  red  and  blue  balls  a  blue  ball  =  |;  .-.the  chance 
of  my  drawing  a  blue  ball  out  of  a  bag  which  contains 
^=iTX7  =  i>  a  result  at  which,  in  this  particular  in- 
stance, I  could  of  course  have  arrived  more  directly. 
Hence,  when  both  premisses  are  affected  by  words  like 
'  probably,'  *  possibly,'  &c.,the  probability  of  the  conclusion 

^  The  truth  of  this  proposition,  with  regard  to  two,  three,  or  any 
nnmber  of  events,  is  proved  at  length  in  Peacock's  Arithmetical 
Algebray  §  469.  *  > 


PROBABLE  REASONING, 


131 


may  always  be  discovered  by  multiplying  together  the  pro- 
babilities of  the  premisses,  the  conclusion  being  therefore 
less  probable  than  either  premiss.      I  append  a  few  in- 
stances of  conclusions  drawn  from  probable  premisses  : — 
(i)  This    plant   will    probably  sprout   up    during   the 
winter  months.     (Let  the  probability  =  f .) 
Whatever  plant  sprouts  up  during  the  winter  will 
probably  be  bitten  by  the  frost.     (Let  the  pro- 
bability =  |.) 
.-.This   plant   may  sprout   up    and    be   frost-bitten. 

(Here  the  probability  =  f  x  4^  =  ^f .) 
.'.The  odds  against  the  event  are  23  to  12,  and  those 
m  favour  of  it  12  to  23. 

(2)  Two  thirds  of  these  men  will  be  enlisted. 
Half  the  men  enlisted  are  killed  in  battle. 

.-.The  probability  of  any  particular  man  being  en- 
listed and  killed  in  battle  =  f  X  J  =  -j. 

.-.It  is  two  to  one  ci gainst  any  partipular  man  here 
being  enlisted  and  killed  in  battle. 

(3)  A  warm  day  may  possibly  be  a  rainy  day.     (Let 

the  probability  =  ^.) 

A  rainy  day   is   probably  a  calm  day.      (Let  the 

probability  =  f .) 

.•.A  warm  day  may  possibly  be  both  rainy  and  calm'^. 

(The  probability  =  j-%.) 

*  I  am  indebted  to  Professor  Shaw,  of  Deny,  for  pointing  out  an 
inaccurac)'  in  the  conclusion  of  this  example,  as  stated  in  the  earlier 
editions,  and  to  Professor  Park  for  the  suggestion  that  it  is  a  pecu- 
liarity of  all  arguments  of  this  kind  that,  strictly  speaking,  both 
premisses  should  be  expressed  in  the  conclusion. 

K  2 


w 


132 


PROBABLE  REASONING, 


N.  B. — It  is  most  important   for  the  student  to  bear 

in  mind  the   ambiguous  use   of  the   words  *  probably/ 

*  probable/    'probability/      The   adverb    'probably'   we 

seem  always  to  use  in  the  sense  of  *  more  likely  than  not/ 

The  adjective  '  probable/  when  employed  as  a  predicate, 

seems  also  to  be  invariably  used  in  the  same  sense ;  thus 

we  say  '  It  is  probable  that  he  will  do  so  and  so/  '  This 

event  is  probable/    But  when  used  to  qualify  a  substantive, 

as  in  such  expressions  'probable   premisses/  'probable 

reasonings,'  &c.,  it  may  be  employed  either  in  the  above 

sense  or  simply  as  contrasted  with  certainty,  and  in  the 

latter  case  the  'probability/  as  we  say,  may  vary  from 

certainty  to  zero.      Lastly,  the  word  'probability'   may 

simply  be  equivalent  to  '  chance,'  as  explained  above,  or 

in  some  expressions  it  may  have  the  meaning  of  *  being 

more  likely  than  not,'  as  when  we  say  '  The  probability 

is  that  he  will  do  so  and  so/     By  '  probable  reasoning' 

at  the  head  of  this  section  I  of  course  mean  reasoning 

which  falls  short  of  certainty,  and  the  value  of  which  may 

vary  to  any  extent  so  long  as  it  does  not  rise  to  certainty 

or  fall  to  zero. 


CORROBORATIVE  EVIDENCE, 


^2^?^ 


On  the  Combination  of  Probable  Arguments, 

[Cumulative  or  Corroborative  Evidence^  including 
Circumstantial  Evidence?^ 

Probable  arguments  may  be  combined  together  in  a 
chain  ^  (or,  as  it  has  been  more  appropriately  called,  a  coil) 
of  reasoning,  each  argument  leading  to  the  same  conclu- 
sion. Instead  of  weakening  each  other,  as  is  the  case 
with  probable  premisses,  such  arguments,  being  all  in- 
dependent testimonies  to  the  truth  of  the  same  conclusion, 
mutually  strengthen  each  other.  If  the  value  of  any 
single  argument  amounts  to  certainty,  the  conclusion 
must  be  true.  In  this  case  therefore  we  have  to  calculate 
the  chances  of  failure  in  each  separate  argument ;  these, 
when  multiplied  together,  give  the  probability  of  all  the 
arguments  together  failing  to  prove  the  conclusion ;  and 
this  fraction,  when  subtracted  from  unity  (which  repre- 
sents certainty),  gives  the  probability,  resulting  from  all 
the  arguments  joindy,  in  favour  of  the  conclusion.  Thus 
suppose  the  probabilities  in  favour  of  certain  probable 
arguments  to  be  represented   respectively  by  \,  |,  f  ; 

^  Chain-reasoning  would  be  the  proper  designation  for  a  series  of 
arguments  (or  links  of  evidence)  which  are  all  inter-dependent,  so 
that,  if  one  argument  fails  (or  one  link  snaps),  the  reasoning  breaks 
down  altogether.  Much  legal  evidence  is  of  this  kind,  as  when 
A  testifies  that  he  received  a  certain  parcel  from  B,  B  that  he 
received  it  from  C,  and  so  on.  In  this  case,  any  one  untrustworthy 
witness  would  invalidate  the  whole  evidence.  On  the  other  hand, 
in  corroborative  evidence  the  various  parts  strengthen  one  another. 


^34 


PROBABLE  REASONING. 


the  chances  of  their  failing  to  prove  the  conclusion  will 
be  represented  Respectively  by  §,  \,  \  (or  the  differences 
between  the  favourable  chances  and  unity);  the  chance 
therefore  of  their  all  failing  to  prove  the  conclusion 
=-  f  X  T  X  T  =  ^V  >*  consequently  the  probability  in  favour 
of  the  conclusion,  as  based  upon  all  the  arguments  jointly, 
is  -j^j,  i.  e.  the  odds  in  favour  of  it  are  29  to  i. 

I  may  illustrate  this  case  by  an  example,  which  will 
also  serve  to  shew  the  characteristic  uncertainty  attaching 
to  this  method  of  reasoning.  Suppose  a  man  to  be 
found  lying  dead  on  a  road  from  the  effects  of  a  wound. 
On  the  same  evening  on  which  he  died,  another  man  was 
seen  running  away  from  the  neighbourhood  of  the  place. 
On  this  man's  house  being  searched,  his  clothes  are  found 
to  be  stained  with  blood;  his  footsteps  correspond  with 
those  leading  to  and  from  the  place  where  the  dead 
man  was  lying;  and  moreover  he  is  known  to  have 
possessed  a  weapon,  now  not  to  be  found,  which  was 
capable  of  inflicting  the  wounds.  The  presumption  in 
favour  of  his  guilt  is  very  great;  each  argument,  taken 
alone,  possesses  some  cogency,  and  when  all  the  argu- 
ments are  taken  together  they  appear  to  be  irresistible. 
But  suppose  the  suspected  man,  when  arrested,  to  give 
this  account  of  the  affair :  he  was  walking  along  the 
road,  armed  with  a  dagger;  he  was  suddenly  attacked 
by  another  man;  a  scuffle  ensued,  and  in  the  scuffle 
he  killed  his  assailant ;  finding  that  he  had  killed  him, 
he  was  seized  with  a  sudden  panic,  threw  away  his 
weapon,  and  ran  home.     Such  an  account,  in  the  case 


CORROBORATIVE  EVIDENCE. 


135 


of  a  timid  and  secretive  man,  might  possibly  be  true, 
and,  in  estimating  the  counter-probabilities,  ;we  should 
have  to  consider  the  characters  of  the  accused  and  the 
dead  man,  and  the  nature  of  the  motive,  if  any,  which 
could  have  led  to  the  supposed  crime.  Suppose  the 
dead  man's  pockets  were  rifled,  and  the  accused  (who 
had  been  previously  convicted  of  a  felony)  were  in 
possession  of  his  money,  there  could  be  little  doubt 
that  he  had  committed  a  murder;  but  suppose  that  the 
character  of  the  accused  was  good,  and  no  likely  motive 
could  be  assigned  for  the  commission  of  the  crime,  his 
own  version  of  the  affair  might  be  accepted  as  probably 
true,  or  at  least  as  throwing  considerable  doubt  on  the 
supposition  of  his  guilt  *. 

*  As  illustrating  the  danger  of  exaggerating  the  value  to  be 
attached  to  this  kind  of  evidence,  I  could  hardly  adduce  a  more 
forcible  example  than  the  following  passage  from  Lord  Coke 
(quoted  by  Bentham"  in  his  Rationale  of  Judicial  Evidence,  Bk.  V. 
ch.  XV.  §  2)  : — 

'  Violenta  presumptio  is  many  times  plena  probatio  ;  as  if  one  be 
run  thorow  the  bodie  with  a  sword  in  a  house,  whereof  he  instantly 
dieth,  and  a  man  is  seen  to  come  out  of  that  house  with  a  bloody 
sword,  and  no  other  man  was  at  that  time  in  the  house.' 

To  this  Bentham  replies  by  two  counter-suppositions : — 

*  I.  The  deceased  plunged  the  sword  into  his  own  body,  as  in  the 
case  of  suicide  ;  the  accused,  not  being  in  time  to  prevent  him,  drew 
out  the  sword,  and  so  ran  out,  through  confusion  of  mind,  for 
chirurgical  assistance. 

*  2.  The  deceased  and  the  accused  both  wore  swords.  The 
deceased,  in  a  fit  of  passion,  attacked  the  accused.  The  accused, 
being  close  to  the  wall,  had  no  retreat,  and  had  just  time  enough  to 
draw  his  sword,  in  the  hope  of  keeping  off  the  deceased ;  the  deceased, 
not  seeing  the  sword  in  time,  ran  upon  it,  and  so  was  killed. 

*  Other  suppositions  might  be  started  besides  these ;  nor  do  these 


136 


PROBABLE  REASONING, 


The  commonest  example  of  evidence  of  this  kind  (which 
may  be  called  Cumulative  or  Corroborative  Evidence)  is 
Circumstantial  Evidence,   so    called   from   the   fact   that 

exculpative  ones  either  of  them  seem  in  any  considerable  degree  less 
probable  than  that  criminative  one :  if  so,  the  probability  of  de- 
linquency, instead  of  being  conclusive,  is  but  as  1  to  2.* 

Sometimes  the  individual  arguments  in  evidence  of  this  kind  are 
of  so  little  value  that,  even  when  several  of  them  are  accumulated, 
they  have  no  practical  force.  '  Presumptio  probabilis,'  Lord  Coke 
says  rightly,  '  moveth  but  little,  but  presumptio  levis  sen  temeraria 
moveth  not  at  all.' 

On  the  other  hand,  the  force  of  this  evidence  may  amount  to  that 
of  moral  certainty.  '  If,'  says  Mr.  Wills,  '  it  be  proved  that  a  party 
charged  with  crime  has  been  placed  in  circumstances  which  com- 
monly operate  as  inducements  to  commit  the  act  in  question, 

that  he  has  so  far  yielded  to  the  operation  of  those  inducements  as 
to  have  manifested  the  disposition  to  commit  the  particular  crime, 
— that  he  has  possessed  the  requisite  means  and  opportunities  of 
effecting  the  object  of  his  wishes,— that  recently  after  the  com- 
mission of  the  act  he  has  become  possessed  of  the  fruits  or  other  con- 
sequential advantages  of  the  crime,— if  he  be  identified  with  the  corpus 
delicti  by  any  conclusive  mechanical  circumstances,  as  by  the  im- 
pressions of  his  footsteps,  or  the  discovery  of  any  article  of  his  apparel 
or  property  at  or  near  the  scene  of  the  crime,— if  there  be  relevant 
appearances  of  suspicion,  connected  with  his  conduct,  person,  or 
dress,  and  such  as  he  might  reasonably  be  presumed  to  be  able,  if 
innocent,  to  account  for,  but  which,  nevertheless,  he  cannot  or  will 
not  explain,— if,  being  put  upon  his  defence  recently  after  the  crime, 
under  strong  circumstances  of  adverse  presumption,  he  cannot  shew 
where  he  was  at  the  time  of  its  commission,— if  he  attempt  to 
evade  the  force  of  those  circumstances  of  presumption  by  false  or 
incredible  pretences,  or  by  endeavours  to  evade  or  pervert  the  course 
of  justice,— the  concurrence  of  all  or  many  of  these  cogent  cir- 
cumstances, inconsistent  with  the  supposition  of  his  innocence  and 
unopposed  by  facts  leading  to  a  counter-presumption,  naturally, 
reasonably,  and  satisfactorily  establishes  the  moral  certainty  of  his 


CIRCUMSTANTIAL  EVIDENCE. 


137 


several  circumstances  are  adduced  as  all  supporting  the 
same  conclusion.  It  will  be  readily  seen  that  the  utmost 
caution  is  required  in  estimating  its  value.  We  are  bound 
to  consider  not  only  the  circumstances  which  point  to 
the  conclusion,  but  also  those  which  make  against  it,  or 
in  favour  of  any  counter-supposition.  It  is  only  when 
we  feel  certain  that  we  have  exhausted  all  possible  sup- 
positions, consistent  with  the  circumstances  of  the  case, 
and  considered  carefully  the  value  of  the  arguments,  or 
series  of  arguments,  pointing  to  each  of  them,  that  we 
are  entided  to  pronounce  with  confidence  in  favour  of 
any  particular  conclusion. 

Any  single  syllogism  in  a  coil  of  circumstantial  evi- 
dence may  be  represented  as  an  argument  with  one 
probable  and  one  certain  premiss,  thus: 

A  man  who  was  seen  running  away,  in  order  to 
escape   observation,  from  the   place  where  the 
dead  man  was  lying,  immediately  after  his  death, 
was  probably  the  murderer, 
This  man  was  seen  running  away,  &c. ; 
.  • .  He  was  probably  the  murderer.  ^ 
The  major  premiss  of  each  of  these  syllogisms  is  the 
result  of  an  analogical  argument;  and  its  value  must  be 
estimated  according    to   the   rules   of  analogy,  already 
explained. 

guilt, — if  not  with  the  same  kind  of  assurance  as  if  he  had  been  seen 
to  commit  the  deed,  at  least  with  all  the  assurance  which  the  nature 
of  the  case  and  the  vast  majority  of  human  actions  admit.'  Wills  on 
Circumstantial  Evidence,  4*^  ed.,  pp.  276,  7. 


138 


PROBABLE  REASONING, 


CIRCUMSTANTIAL  EVIDENCE. 


139 


Note  I.— It  is  more  usual  to  regard  the  separate  syllo- 
gisms in  a  coil  of  circumstantial  evidence  as  syllogisms 
in  the  second  figure,  involving  an  undistributed  middle, 
and  justifying  a  probable  conclusion.  Thus  the  above 
syllogism  would  be  represented  in  the  form  : 

The   murderer  would,   to   escape   observation,   run 

away,  &c., 
This  man,  to  escape  observation,  ran  away,  &c. ; 

.-.This  man  is  probably  (or  possibly)  the  murderer. 
It  seems  however  extremely  awkward  to  represent  such 
reasonings  as  fallacies,  and  then,  by  way  of  compensation, 
to  regard  them  as  probable  arguments.  This  mode  of 
treatment,  no  doubt,  originated  in  the  desire  to  conform 
the  arguments  in  circumstantial  evidence  to  those  Enthy- 
mematic  syllogisms  of  Aristotle  which  employ  the  o-jy^elov 
in  the  second  figure.  For  an  account  of  the  Enthymeme 
and  its  subdivisions,  the  student  is  referred  to  Trendelen- 
burg's Elements,  §  37,  and  Dr.  Mansel's  Appendix  to 
Aldrich,  Note  F. 

Note  2. — There  are  some  cases,  as,  for  instance,  those 
in  which  the  witnesses  may  be  suspected  of  lying,  or  in 
which  they  are  actuated  by  violent  passions,  where  circum- 
stantial evidence  may  be  of  far  greater  value  than  direct 
evidence.  See  some  remarks  on  this  subject  in  an  article 
contributed  to  the  Fortnightly  Review  for  January,  1873, 
by  Sir  H.  Maine,  and  since  reprinted  at  the  end  of 
Village  Communities,  On  circumstantial  evidence,  gene- 
rally, the  student  would  do  well  to  consult  Sir  Fitzjames 
Stephen's  Introduction  to  the  Indian  Evidence  4ct,  Wills 


on  Circumstantial  Evidence  '\  and  Taylor's  Treatise,  on  the 
Law  0/  Evidence,  Pt.  I.  ch.  4.  In  Direct  Evidence,  the 
witness  testifies  to  the  precise  fact  alleged ;  in  Indirect  or 
Circumstantial  Evidence  to  some  fact  or  facts  indicative 
of  the  fact  alleged.  The  rules  for  estimating  the  logical 
value  of  circumstantial  evidence  apply  also  to  direct  evi- 
dence in  all  those  cases  in  which  we  have  any  reason  for 
questioning  either  the  veracity  or  the  competence  of  the 
principal  witness,  and  in  which,  therefore,  his  evidence 
requires  corroboration  from  independent  testimony. 

*  The  work  of  Mr.  Wills  is  exceedingly  interesting  and  instructive ; 
but  the  reader  must  be  on  his  guard  against  an  erroneous  statement 
on  the  mathematical  value  of  a  coil  of  circumstantial  evidence. 


— j^-s^a'jfe^^t^-^' 


CHAPTER    VIII. 
On  Fallacies, 

§  1.  A  FALLACY  is,  strictly  speaking,  a  defective 
inference,  but  the  word  is,  by  common  usage,  extended 
to  any  error  either  in  the  premisses  or  in  the  conclusions 
of  our  arguments.  In  deductive  Logic  (for  we  are  not 
here  concerned  with  the  fallacies  incident  to  induction  ^ 

1  The  fallacy  of  False  Analogy  (which  consists  either  in  over- 
estimating, in  some  particular  case,  the  value  of  the  argument  from 
analogy,  or  in  supposing  an  analogy  where  none  exists)  falls 
properly  within  the  domain  of  Inductive  Logic,  and  is  discussed  in 
the  author's  *  Elements  of  Inductive  Logic,'  ch.  vi.  It  is  not  to  be 
confounded  with  the  fallacy  arising  from  the  employment  in  a 
syllogism  of  a  word  used  analogously,  as  if  it  were  used  univocally, 
which,  as  already  noticed,  is  one  case  of  the  fallacy  of  ambiguous 
terms.  Thus  to  argue,  because  there  are  certain  points  of  re- 
semblance between  the  development  of  the  individual  and  the 
development  of  the  race,  that,  therefore,  since  the  individual  dies, 
the  race  will  probably  die  also,  or,  because  there  are  certain  points  of 
resemblance  between  the  earth  and  the  other  planets,  that,  therefore, 
the  other  planets  are  certainly,  or  very  probably,  inhabited,  would 
both  be  instances  of  false  analogy,  the  former  being  the  assumption 
of  an  analogy  which  appears  to  have  no  existence,  the  latter  being 
an  exaggeration  of  the  value,  in  that  particular  case,  of  the  probable 
argument.  But  to  argue,  because  art  (i.  e.  artistic  skill)  requires  the 
highest  intellectual  gifts,  and  dissimulation  is  art  (i.e.  deceit),  that, 
therefore,  dissimulation  requires  the  highest  intellectual  gifts,  is 
obviously  a  mere  play  upon  words,  and  owes  its  semblance  of  reason- 
ing simply  to  the  ambiguity  of  language. 


FALLACIES. 


141 


or  to  the  operation  subsidiary  to  it,  observation)  these 
errors  are  traceable  to  one  of  four  sources :  the  assump- 
tion of  a  false  premiss,  neglect  of  the  laws  of  deductive 
inference,  irrelevancy,  and  ambiguity  of  language.  Any 
conclusions,  therefore,  or  series  of  conclusions,  which 
transgress  no  law  of  inference,  which  are  derived  from 
true  premisses,  which  are  relevant  to  the  matter  under 
discussion,  and  which,  with  their  premisses,  are  expressed 
in  unambiguous  language,  may  be  regarded  as  faultless. 

§  2.  I.  A  false  premiss,  borrowed  from  some  science 
which  is  not  under  investigation,  can  only  be  detected  by 
a  special  knowledge  of  the  science  from  which  it  is  taken. 
Many  fallacies,  described  in  the  old  books  on  Logic,  are 
really  instances  of  the  assumption  of  a  false  premiss,  and 
therefore  specially  concern  other  sciences  rather  than 
logic.  Thus  the  celebrated  fallacy  of  Achilles  and  the 
tortoise  (see  p.  175)  rests  upon  a  false  assumption,  viz. 
that  when  the  distances  between  the  two  become  infini- 
tesimal they  will  be  traversed  by  Achilles  in  finite  and  equal 
(and  not,  as  will  actually  be  the  case,  in  infinitesimal  and 
rapidly  diminishing)  times. 


The  phrase  '  False  Analogy '  is  also  applied  to  a  perversion  of  the 
Analogy  of  Aristotle  (see  p.  72)  ;  namely,  to  those  cases  in  which 
the  conclusion  is  based  upon  relations  wherein  the  two  sets  of  terms 
compared  do  not  agree.  Thus,  though,  in  many  respects,  the  relation 
of  a  king  to  his  subjects-  is  the  same  as  that  of  a  father  to  his 
children,  it  is  plain  that  invalid  conclusions  might  be  based  on  this 
general  relation,  by  extending  it  to  points  in  which  it  does  not 
subsist.  Such  invalid  conclusions  would  be  called  'False  Ana- 
logies.* 


143 


FALLACIES. 


§  3.  II.  The  fallacies  due  to  the  neglect  of  the  laws 
of  deductive  inference  (which,  strictly  speaking,  are  the 
only  fallacies  to  be  detected  by  a  mere  knowledge  of 
Deductive  Logic)  have  already,  to  some  extent,  been 
discussed.  The  principal  sources  of  fallacy  in  a  single 
inference  are  illicit  process  and  undistributed  middle. 

Undistributed  middle  often  occurs  in  the  following 
form : 

All   Conservatives   (or   Liberals,    Roman  Catholics, 
Protestants,   Englishmen,   Frenchmen,  &c.)    hold 
such  and  such  opinions,  do  such  and  such  things, 
or  possess  such  and  such  characteristics; 
A  B  holds  such  and  such  opinions,  does  such  and 
such  things,  or  possesses  such  and  such  charac- 
teristics ; 
.  • .  A  B  is  a  Conservative  (Liberal,  Roman  Catholic,  &c.). 
We  might,  of  course,  argue  quite  as  legitimately  that, 
because  both  men  and  cats  are  animals,  all  men  are  cats. 
If,  however,  the  argument  assumed  this  shape, — 

None  but  Liberals  (Roman  Catholics,  &c.)  hold  such 

and  such  opinions,  or  do  such  and  such  things ; 
This  man  holds  such   and  such  opinions,  or  does 
such  and  such  things; 
.'.He  is  a  Liberal  (Roman  Catholic,  &c.), 
it  would  be  perfectly  legitimate. 

The  major  premiss  in  this  case  (see  p.  83)  is  equivalent 
to  the  proposition  *A11  men  who  hold  such  and  such 
opinions,  or  do  such  and  such  things,  are  Liberals  (Roman 
Catholics,  &c.).'    As  was  shewn  in  the  Chapter  on  Proba- 


FALLACIES, 


143 


bilities,  we  might  also  advance  a  perfectly  legitimate,  argu- 
ment of  the  following  kind :  '  A  man  who  holds  such 
and  such  opinions,  or  does  such  and  such  things,  is 
probably  a  Liberal  (Roman  Catholic,  &c.) ;  this  man  holds 
such  and  such  opinions,  or  does  such  and  such  things; 
therefore  he  is  probably  a  Liberal  (Roman  Catholic,  &c.).' 
Of  Illicit  Process  the  following  syllogisms  may  serve  as 
examples : 

No  form  of  democracy  excludes  the  great  mass  of 

the  people  from  political  power. 
Any  form  of  government  which  excludes  the  great 
mass  of  the  people  from  political  power  is  subject 
to  violent  revolutions ; 
.'.No  form  of  democracy  is  subject  to  violent  revo- 
lutions. 
The  early  history  of  some  nations  is  full  of  incredible 

events, 
A  history  which  is  full  of  incredible  events  is  not 

worthy  of  serious  study ; 
.'.The  early  history  of  any  nation  is  not  worthy  of 
serious  study. 
The  former  syllogism  (AEE  in  the  first  figure)  involves 
illicit  process  of  the  major,  the  latter  (EIE  in  the  first 
figure)  illicit  process  of  the  minor.     It  will  be  observed 
that  the  various   propositions  are   not  stated  in  strictiy 
logical  form,  though  they  easily  admit  of  being  so  stated, 
and    the   premisses   of  both    syllogisms   require    to   be 
transposed. 

Where  there  is  a  long  train  of  reasoning  in  which  one 


144 


FALLACIES, 


syllogism  is  employed  to  prove  the  premiss  of  another, 
and  so  on,  a  fallacy  frequently  occurs,  which  often 
escapes  detection.  This  is  called  the  Argument  in  a 
Circle,  A  book  is  written,  or  a  speech  is  made,  with  the 
object  of  proving  some  controverted  opinion.  The  author 
or  speaker,  being  full  of  one  idea,  after  a  litde  preliminary 
matter,  assumes  the  proposition  to  be  proved,  slightly  dis- 
guised, probably,  under  some  equivalent  form ;  from  this 
proposition  he  deduces  various  conclusions,  and  these 
conclusions,  when  put  together,  of  course  triumphantly 
establish,  from  various  sides,  his  view  of  the  controversy. 
This  is  not  an  unfair  analysis  of  many  elaborate  argu- 
ments, the  fallacy  being,  in  the  great  majority  of  in- 
stances, undesigned,  and  imposing  on  the  author  or 
speaker  himself  quite  as  much  as  on  his  readers  or 
hearers.  The  fallacy,  when  expressed  in  its  naked  form, 
may  be  described  as  the  assumption,  in  a  train  of  reason- 
ing, of  the  conclusion  of  a  subsequent  syllogism  as  a 
premiss  of  a  precedent  syllogism.  It  may  be  represented 
thus: — 

Syll.  (i)     Bis  A,  Syll.  (2)     C  is  A, 

C  is  B ;  B  is  C  ; 

.'.C  is  A.  .-.B  is  A. 

Thus,  when  asked  why  B  is  A,  we  reply,  because  C  is 
A;  and  when  asked  why  C  is  A,  we  reply,  because  B  is  A. 

Of  course,  in  actual  argument,  hundreds  of  interme- 
diate syllogisms  might  occur  between  syll.  (i)  and  syll.  (2). 
The  larger  the  number  of  intermediate  steps,  the  more 
likely  is  the  fallacy  to  escape  detection,  and,  conversely, 


FALLACIES. 


145 


the  true  mode  of  exposing  the  fallacy,  as  Whately 
observes,  is  to  narrow  the  circle  by  cutting  out  the 
intermediate  steps,  and  exhibiting  the  assumption  of 
the  conclusion  in  its  naked  form.  The  fallacy  is  to  be 
regarded  as  a  breach  of  the  laws  of  inference,  because, 
when  reduced  to  its  simplest  terms,  it  is  a  proving  of 
the  conclusion  by  means  of  itself,  instead  of  by  means 
of  premisses  which  jointly  necessitate  it.  But,  unlike  the 
fallacies  of  illicit  process,  &c.,  already  treated,  it  cannot 
be  detected  from  the  inspection  of  a  single  syllogism,  but 
requires  the  comparison  of  two  syllogisms  or  more. 

The  argument  in  a  circle  is  the  most  important  case  of 
the  fallacy  called  Petitio  Principii  (or,  as  it  is  more 
properly  called,  Petitio  Qucesiti,  begging  the  question). 
The  other  cases  of  petitio  principii  generally  enumerated, 
though  the  enumeration  is  by  no  means  exhaustive,  are 
(2)  when  the  conclusion  simply  re-asserts  a  premiss  of  the 
same  syllogism-,  (3)  when  it  is  exactly  synonymous  with** 


II 


*  If  a  syllogism,  in  which  one  of  the  simpler  forms  of  petitio 
principii  occurs,  were  stated  at  length,  one  of  the  premisses  wonld 
be  otiose  (i.e.  would  not  contribute  towards  the  conclusion),  but, 
as  already  noticed,  in  our  reasonings,  as  actually  expressed,  we 
generally  suppress  one  of  the  premisses. 

^  *  The  English  language,'  says  Archbishop  Whately  {^Elements  of 
Logic,  Bk.  III.  §  13),  '  is  perhaps  the  more  suitable  for  the  fallacy 
ai  petitio  principii,  from  its  being  formed  from  two  distinct  lan- 
guages, and  thus  abounding  in  synonymous  expressions  which  have 
no  resemblance  in  sound  and  no  connexion  in  etymology ;  so  that  a 
sophist  may  bring  forward  a  proposition  expressed  in  words  of  Saxon 
origin,  and  give  as  a  reason  for  it  the  very  same  proposition  stated 
in  words  of  Norman  origin ;  e.g.  "to  allow  every  man  an  unbounded 

L 


146 


FALLACIES, 


FALLACIES. 


147 


one  of  the  premisses,  (4)  when  one  of  the  premisses  is 
equally  unknown  with  the  conclusion,  (5)  when  it  is  more 
unknown.  Cases  (4)  and  (5)  are  really  instances  of  the 
assumption  of  a  false  premiss,  or  at  least  of  a  premiss 
which  is  not  known  to  be  true.  Cases  (2)  and  (3)  arise 
from  a  neglect  of  the  laws  of  syllogism,  for,  instead  of 
proving  the  conclusion  from  the  two  premisses  jointly^  we 
simply  re-assert  one  of  the  premisses  ■*. 

Connected  with  this  fallacy  is  the  rhetorical  device  of 
question-begging  epithets.  [  Thus,  though  the  matter  we  are 
discussing  is  open  to  dispute,  we  may  speak  of  a  ne- 
farious project,  a  laudable  ambition,  an  astute  act,  a  far- 
sighted  policy,  and  so  on,  attempting,  by  means  of  a 
carefully-selected  epithet,  to  assume  the  point  at  issue,  or 
at  least  to  create  an  unfair  prejudice  in  the  mind  of  the 
hearer  or  reader  whom  we  address.  \ 

freedom  of  speech  must  always  be,  on  the  whole,  advantageous  to 
the  State ;  for  it  is  highly  conducive  to  the  interests  of  the  com- 
munity that  each  individual  should  enjoy  a  liberty,  perfectly  un- 
limited, of  expressing  his  sentiments."  * 

*  It  has  sometimes  been  maintained  that  every  syllogism  is  a 
petitio  principii.  Of  course  the  controversy  entirely  turns  upon  the 
meaning  of  the  terms,  but,  according  to  the  account  I  have  given  of 
the  two,  a  syllogism  is  so  far  from  being  a  petitio  principii,  that 
every  petitio  principii  is  a  distinct  breach  of  the  laws  of  syllogism. 
TTie  conclusion  of  a  syllogism  is  indeed  implied  by  the  two  premisses 
taken  in  combination,  and  is,  in  fact,  the  compression  into  a  single 
proposition  of  what,  as  premisses,  were  two  distinct  propositions, 
but,  in  a  petitio  principii,  the  conclusion  is  merely  a  re-assertion  of 
one  of  the  premisses  ;  in  the  simpler  cases,  of  a  premiss  in  the  same 
syllogism  ;  in  the  argument  in  a  circle,  of  a  premiss  in  one  of  the 
preceding  syllogisms  of  the  series. 


§  4.  III.  The  fallacy  of  Irrelevancy  (or,  as  it  is  some- 
times called,  shifting  ground)/ is  technically  termed  Igno- 
ratio  Elenchi,  i.  e.  ignorance  of  the  syllogism  required  for 
the  refutation  of  an  adversary.  Thus,  in  the  strictest 
sense  of  the  words,  ignoratio  elenchi  is  committed  by  a 
person  who  in  a  disputation  does  not  confine  himself  to 
proving  the  contradictory  or  contrary  of  his  adversary's 
assertion,  or  who  proves  a  proposition  other  than  the 
contradictory  or  contrary.  But,  like  many  other  terms 
borrowed  from  the  dialectical  disputations  of  the  ancients, 
this  has  now  received  a  wider  meaning.  Whenever  an 
argument  is  irrelevant  to  the  object  which  a  speaker  or 
writer  professes  to  have  in  view,  it  is  called  an  ignoratio 
elenchi.  vTlius,  if  I  am  endeavouring  to  convince  a  person 
that  some  particular  measure  is  for  his  personal  interest, 
and  I  adduce  arguments  to  prove  that  it  contributes  to 
the  general  utility,  or  that  it  is  the  necessary  consequence 
of  other  acts  of  legislation,  I  am  guilty  of  an  ignoratio 
elenchi,  as  I  should  also  be  if,  when  it  was  my  object 
to  establish  either  of  the  other  two  conclusions,  I  were 
to  appeal  to  his  personal  interest.  When  the  question 
at  issue  is  the  truth  of  an  opinion,  it  is  an  ignoratio 
elenchi  to  attack  it  for  its  novelty,  or  for  its  coming  from 
a  foreign  source,  or  for  any  supposed  consequences 
which  may  result  from  it,  or  to  try  to  throw  discredit  on 
its  author  by  saying  that  it  has  often  been  started  before, 
and  so  is  no  discovery  of  his. 

This  fallacy  is  more  common  in  spoken  addresses  than 
in  books,  as  the  feelings  both  of  speaker  and  hearers 

L  2 


A 


148 


FALLACIES, 


being  more  excited,  and  their  judgment  less  critical,  they 
are  less  likely  to  insist  on  relevancy  of  argument.     On 
such  occasions  it  most  commonly  takes  the  form  of  an 
argumentum  ad  hominem ,rwhereby  the  speaker,  in  support 
of  the  truth  of  his  assertions,  or  to  throw  discredit  on 
an  adversary,  appeals,  not  to  the  unbiassed  judgment  of 
his  auditors,  but  to  their  passions,  interests,  prejudices, 
sentiments  and  associations.     The  argumentum  ad  homi- 
nem, however,  is  not  confined  to  set  speeches;  it  some- 
times occurs  in  writings,  and  frequently  in  debates.     In 
the  latter,  it  often  assumes  the  shape  of  an  appeal  to  the 
previous  acts,  or  the  previously  expressed  convictions  of 
the  opponent;  '  That  measure,  or  that  argument,  or  that 
proposal  does  not  come  well  from  you,  who  once  pro- 
posed such  a  measure,  or  expressed  such  an  opinion,  or 
advanced  such  an  argument,  or  did  such  and  such  acts.' 
There  are  occasions  when  the  argumentum  ad  hominem 
may  legitimately  be  used   as   a  retort,   but  it  must  be 
advanced  as  such,  and  not  as  an  argument.     It  is  so 
called  in  opposition  to  the   argumentum  ad  rem  or  ad 
judicium.      Similar   phrases  are  used   to   express  other 
forms  of  the  ignoratio  elenchi,  as  e.g.  the  argumentum 
ad  verecundiam,  argumentum  ad  baculum^  &c.     The  argu- 
mentum ad  populum  I  have  treated  as  identical  with  the 
argumentum  ad  hominem;  if  called  on  to  distinguish  them, 
which   seems   unnecessary,    I   should    refer   the   first  to 
addresses  made  in  the  presence  of  a  large  auditory,  the 
second  to  disputations  with  one  or  a  few  individuals  ®. 
^  The   student   will   find  some  amusing  examples  of  ignoratio 


% 


FALLACIES, 


149 


§  5.  IV.  The  fallacy  originating  in  ambiguity  of 
language  I  noticed  when  warning  the  student  against 
the  employment  of  equivocal  terms.  This  fallacy  (whe- 
ther we  call  it  that  of  equivocal  terms,  of  ambiguous 
terms,  or  of  ambiguity  of  language)  of  course  includes 
fallacies  arising  from  any  ambiguity  which  may  attach 
to  the  quantity  of  the  subject,  as  e.  g,  the  fallacy  arising 
from  the  ambiguous  use  of  the  word  '  all/  which  will  be 
noticed  below. 

I  now  proceed  to  notice  one  or  two  common  cases 
of  this  fallacy.  The  same  term  may  often  be  used  in 
one  place  distributively  and  in  another  collectively,  and 
we  may  argue  as  if  the  term  in  both  places  had  the  same 
meaning.  /This  is  called  the  fallacy  of  Composition^ox 
Division  ;  of  composition,  if  we  argue  from  a  term  taken 
distributively  as  if  it  were  taken  collectively;  of  division, 
if  we  argue  from  a  term  taken  collectively  as  if  it  were 
taken  distributively.  Thus  (to  give  common  instances) 
7  and  2  are  (distributively)  odd  and  even,  nine  is  7 
and  2  (collectively) ;  . ' .  nine  is  odd  and  even.  Here 
we  argue  from  7  and  2  taken  distributively,  as  if  they 
had  been  taken  collectively,  and  the  fallacy  is  one  of 
composition.  Five  is  one  number,  3  and  2  (collectively) 
are  five;  .-.3  and  2  (distributively)  are  one  number. 
Here  the  fallacy  is  one  of  division.  Again,  The  people 
of  England  have  a- prejudice  against  the  French,  he  is 
one  of  the  people  of  England ;    .  • .  he  has  a  prejudice 

elenchi,  or  irrelevant  argument,  in  Sydney  Smith's  well-known  jeu 
d'esprit,  the  Noodle's  Oration. 


i 


I 


150 


FALLACIES. 


against  the  French.  The  major  premiss  might  be  quite 
true,  and  still  the  particular  man  spoken  of  might  have 
a  strong  sympathy  with  the  French,  and  be  a  warm 
admirer  of  their  institutions.  Here  we  argue  from  the 
term  *  people,'  taken  collectively,  as  if  it  had  a  distribu- 
tive signification  and  whatever  were  predicable  of  the 
English  people  might  be  predicated  of  every  single  in- 
dividual amongst  them;  hence  the  fallacy  is  one  of 
division.  The  last  instance  is  an  example  of  a  very 
common  source  of  deception.  A  certain  people,  corpo- 
ration, or  society,  in  its  collective  capacity,  has  certain 
characteristics,  has  performed  certain  acts,  passed  cer- 
tain resolutions,  or  is  known  to  have  expressed  certain 
sentiments;  hence  it  is  unreflectingly  supposed  that  any 
particular  individual  belonging  to  the  class  has  the  same 
characterisdcs,  participates  in  the  same  sentiments,  and 
has  joined  in  the  same  acts.  In  many  cases,  of  course, 
he  may  be  a  strong  dissentient,  and  may  have  actively 
opposed  the  measures  adopted. 

The  ambiguous  use  of  the  word  '  all '  furnishes  a  good 
instance  of  the  fallacies  of  composition  and  division.  We 
may  argue  from  *  all/  meaning  all  taken  together,  as  if 
it  meant  all  severally,  and  thus  commit  the  fallacy  of 
division ;  or  from  *  all,'  meaning  all  severally,  as  if  it 
meant  all  taken  together,  and  thus  commit  the  fallacy  of 
composition.  Thus,  when  I  say,  *  All  these  boxes  weigh 
so  much/  or  '  All  these  men  can  eat  so  much,'  I  leave  it 
doubtful  whether  I  mean  all  taken  together  or  all  taken 
severally.    The  ambiguity  may  be  removed  by  substituting 


FALLACIES. 


151 


for  the  word  *  all/  when  used  in  a  distributive  sense, '  every,' 
and,  when  used  in  a  collective  sense,  *  the  whole  of.' 

Another  pair  of  fallacies  which  falls  under  the  head  of 
'  ambiguous  terms '  is  the  pair  known  as  the  Fallacia 
\Accidentis  (or  the  Fallacia  a  dido  simpUciter  ad  dictum 
secundum  quid)  and  the  Fallacia  a  dido  secundum  quid  ad 
dictum  simpUciter,  In  the  first  we  argue  from  what  is 
true  as  a  general  rule  (i.  e.  unless  there  be  some  modi- 
fying circumstances)  as  if  it  were  true  under  all  circum- 
stances; in  the  second  from  what  is  true  under  certain 
special  circumstances  as  if  it  were  true  as  a  general 
rule.  Thus  a  particular  walk  may  be  an  agreeable 
one,  but  it  does  not  follow  that  it  would  be  so  in 
wet  or  windy  weather;  plain-speaking,  frugality,  gene- 
rosity, may  all  be  virtues,  but  it  does  not  follow  that 
it  would  be  virtuous  to  practise  them  on  all  possible 
occasions.  Or,  to  take  instances  of  the  second  fallacy, 
a  political  revolution  may,  under  particular  circum- 
stances, be  necessary  to  the  welfare  or  existence  of  a 
country,  but  it  does  not  follow  that  a  ^tate  of  society, 
in  which  political  revolutions  are  frequent,  is  either 
necessary  or  desirable;  it  may  be  necessary  if  I  am 
suffering  from  a  particular  disease  that  I  should  take 
opium  or  abstain  from  labour,  but  it  does  not  follow 
that  these  practices  would  be  good  for  me  when  I  am 
restored  to  health.  The  fallacies  are  due  to  our  not 
sufficiently  qualifying  the  terms  which  we  use,  and,  by 
insisting  on  precision  of  language,  they  may  always  be 
avoided. 


i 


I 


's 


152 


FALLACIES, 


Though  the  definitions  I  have  given  of  this  pair  of 
fallacies  are  conformable  to  the  usage  of  most  modern 
logicians  ^  and  are  stated  in  a  form  which  is  most  likely 
to  be  of  practical  service  to  the  student,  they  do  not 
exactly  correspond  with  the  original  meaning  of  the 
expressions.  The  '  Fallacia  Accidentis '  and  the  *  Fallacia 
a  dicto  secundum  quid  ad  dictum  simpliciter/  according 
to  their  original  usage,  applied  to  those  cases  in  which  a 
term,  when  not  implying  accidents,  was  confounded  with 
the  same  term,  when  implying  accidents.  Thus,  to  take 
the  common  instance  (which  is  sufficiently  absurd) :  '  What 
you  buy  in  the  market  you  eat ;  raw  meat  is  what  you 
buy  in  the  market ;  .  • .  raw  meat  is  what  you  eat/  Here 
it  may  be  replied  that  what  we  buy  in  the  market  we  do 
indeed  eat,  but  not  necessarily  in  the  same  state  in  which 
we  buy  it   at   market"^.     This  particular  instance  is  an 

*  As,  for  instance,  Mill  {Logic,  Bk.  V.  ch.  vi.  §  4),  Port  Royal 
Logic  (Part  III.  ch.  xix.  §  5,  7).  The  latter  virtually  treats  both 
fallacies  as  if  they  were  a  dicto  secundum  quid  ad  dictum  simpliciter. 

''  Mr.  de  Morgan  adduces  one  of  Boccaccio's  stories  as  affording 
an  amusing  instance  of  the  fallacia  accidentis.  It  is  the  old  example 
of  the  *  raw  meat '  in  another  form  : — 

*  A  servant  who  was  roasting  a  stork  for  his  master  was  prevailed 
upon  by  his  sweetheart  to  cut  off  a  leg  for  her  to  eat.  When  the 
bird  came  upon  table,  the  master  desired  to  know  what  was  become 
of  the  other  leg.  The  man  answered  that  storks  had  never  more 
than  one  leg.  The  master,  very  angry,  but  determined  to  strike  his 
servant  dumb  before  he  punished  him,  took  him  next  day  into  the 
fields  where  they  saw  storks,  standing  each  on  one  leg,  as  storks  do. 
The  servant  turned  triumphantly  to  his  master,  on  which  the  latter 
shouted,  and  the  birds  put  down  their  other  legs  and  flew  away.  "  Ah, 
sir,"  said  the  servant,  "you  did  not  shout  to  the  stork  at  dinner 


FALLACIES, 


^5i 


example  of  the  Fallacia  Accidentis.  From  their  technical 
meaning,  these  fallacies  would  easily  pass  into  their  pre- 
sent signification,  which  is  both  more  intelligible  and  of 
greater  practical  service. 

I  may  notice  one  more  example  of  the  errors  due 
to  ambiguous  language,  viz.  the  fallacy  of  what  may  be 
called  Paronymous  Terms.  The  same  word  may  often 
assume  different  forms,  as  substantive,  adjective,  adverb, 
or  verb,  but  it  does  not  follow,  when  it  has  assumed 
these  different  forms,  that  they  all  retain  corresponding 
meanings.  It  has  been  already  noticed  that  the  words 
probably,  probable,  probability,  though  the  two  last  are 
themselves  ambiguous,  vary  in  meaning  according  as  we 
use  the  adverb,  the  adjective,  or  the  substantive.  Thus, 
if  I  hear  some  one  ask  the  question  '  What  is  the  pro- 
bability of  my  throwing  an  ace  with  a  die  at  a  single 
throw?'  I  cannot  infer  that  in  any  single  throw  I  shall 
probably  throw  an  ace.  Again,  because  a  man  has  done 
something  unjust  (i.e.  has  committed  an  act  which  in 
its  results  is  unjust),  I  cannot  infer  that  he  has  acted  un- 
justly (i.  e.  with  intentional  injustice),  nor,  even  if  he  has 
acted  unjustly  (i.  e.  in  one  or  more  instances),  can  I  infer 
that  he  is  an  unjust  man  (i.  e.  a  man  of  unjust  habits  or 
character).  To  take  an  old  instance,  because  projectors 
are  unfit  to  be  trusted,  and  this  man  has  formed  a  pro- 
ject, it  does  not  follow  that  he  is  unfit  to  be  trusted. 
Nor  from  the  meaning  attached  to  the  expressions,  kingly, 

yesterday ;  if  you  had  done  so,  he  would  have  shewn  his  other  leg 
too.'" 


!! 


154 


FALLACIES. 


nobly,  gentlemanly,  can  we  argue  to  the  usual  qualities 
of  a  king,  a  nobleman,  or  a  gentleman ;  nor,  on  the 
meanings  of  the  words  '  to  trow,'  *  to  represent,'  can  we 
base  any  sound  argument  as  to  the  nature  of  truth,  or 
the  duties  of  a  representative.  All  instances  of  this  fal- 
lacy, when  stated  syllogistically,  involve  four  terms,  and 
so  offend  against  the  rules  for  the  construction  of  a 
syllogism,  but,  as  we  do  not  ordinarily  state  our  argu- 
ments in  a  syllogistic  shape,  and  these  fallacies  undoubt- 
edly impose  on  us  through  the  ambiguity  of  language, 
it  is  better  to  consider  them  here  rather  than  under  the 
second  head. 

Many  other  forms  of  fallacy  may  be  regarded  as  due 
to  ambiguities  of  language,  but  it  has  perhaps  been  the 
tendency  of  modern  logicians,  and  especially  of  Whately, 
to  overload  this  division  of  fallacies,  and  to  treat  as  merely 
differences  of  language  what  are  in  reality  radical  differ- 
ences of  opinion.  At  the  same  time  it  cannot  be  denied 
that  terms  expressive  of  fundamental  conceptions  in  their 
several  sciences,  such  as  faith,  church,  election,  law,  loyalty, 
federation,  justice,  value,  capital  force,  nature,  natural,  &c., 
are  frequently  used,  in  the  same  discussion,  in  the  most 
widely  divergent  senses,  and  are  consequently  the  source 
of  endless  confusion  in  our  reasonings.     Thus  the  term 

*  faith '  may  mean  either  a  belief  m  certain  propositions,  or 
confidence  J  trust,  and  repose  in  a  certain  person ;  the  word 

*  church '  may  mean  the  whole  body  of  Christians  (and, 
of  course,  in  this  sense  its  signification  will  vary  accord- 
ing to  the  meaning  attached  to  the  term  Christian),  a 


FALLACIES, 


155 


particular  section  of  Christians,  a  congregation  meeting 
in  a  certain  place,  the  place  of  meeting,  and,  lastly, 
by  a  strange  perversion  of  the  term,  the  clergy  as  dis- 
tinguished from  the  laity ;  the  term  '  loyalty '  may  mean 
either  attachment  to  the  laws  of  a  country  in  general, 
special  attachment  to  some  particular  portion  of  the  laws, 
or,  in  its  most  restricted  sense,  personal  attachment  to  the 
supreme  ruler ;  '  capital '  may  mean  either  the  amount  of 
money  possessed  by  a  trader,  or  his  whole  stock  of 
commodities  available  for  future  production ;  '  natural ' 
may  express  either  the  original  condition  of  a  thing,  or 
the  state  into  which  it  is  ultimately  developed,  besides 
having  countless  other  meanings.  On  account  of  the 
various  significations  which  may  be  attached  to  the  same 
term,  it  is  necessary,  in  entering  on  any  investigation, 
carefully  to  define  the  terms  to  be  employed,  and  never, 
without  express  notice,  to  deviate  from  the  sense  thus 
imposed  upon  them  ^ 

'  The  so-called  '  Fallacia  plurium  interrogationum '  has  not  been 
noticed  in  the  text,  because  it  is  a  rhetorical  artifice,  rather  than 
a  logical  fallacy.  It  consists  in  covertly  putting  as  a  single  question 
what  is  in  reality  two,  as  for  instance,  *  Are  gall  and  honey  sweet  ?  * 
*  Have  you  cast  your  horns  ?  '  (known  as  *  comutus  ').  *  What  did 
you  take,  when  you  broke  into  my  house  last  night  ?  '  *  Have  you 
given  up  beating  your  father  ? '  The  object  is  to  entrap  the  re- 
spondent into  an  admission  which  he  would  otherwise  not  be  likely 
to  make. 


!|^ 


CHAPTER  IX. 


■u 
'm9 


On  Method  as  applied  to  the  arrangemefit  of 
Syllogisms  in  a  Train  of  Reasoning. 

I  DO  not  propose  to  treat  of  Method  in  general  (for 
this  would  involve  a  discussion  of  induction  and  the  various 
relations  in  which  it  stands  to  deductive  inference),  but  it 
may  be  useful  to  the  student  if  I  offer  a  few  remarks  on 
Method  under  the  limitation  stated  in  the  heading  of  this 
chapter.  When  syllogisms  are  combined  in  a  train  of 
reasoning,  we  may  either  commence  with  the  conclusion, 
and  ask  what  reasons  we  have  for  believing  it,  and  then  go 
on  to  ask  the  reason  for  believing  the  premisses,  and  so 
on,  till  at  last  we  arrive  at  some  propositions  of  which  there 
is  no  doubt,  or  in  which  we  at  least  can  acquiesce ;  or 
else  we  may  follow  the  reverse  process,  and  commencing 
with  propositions  which  are  the  result  of  some  previous 
investigation,  or  which  we  at  all  events  accept  as  true, 
may  go  on  combining  them  with  each  other,  till  at  last 
we  arrive  at  some  conclusion  which  we  regard  as  suffi- 
ciently important  to  terminate  our  enquiries.  The  former 
method  will  be  familiar  to  my  readers  as  that  by  which 
we  solve  what  are  called  'geometrical  deductions,'  and 
in  fact  as  the  method  which  we  generally  though  not 


ANALYTICAL  AND  SYNTHETICAL  METHODS,  157 


universally  employ  when  we  are  attempting  to  resolve 
difficulties  for  ourselves;  the  latter  as  the  method  by 
which  the  propositions  in  Euclid  are  proved,  and  in 
fact  as  the  method  which  we  generally  though  not  uni- 
versally employ,  when  it  is  our  object  to  teach  others, 
either  orally  or  by  book.  Now  the  former  method  is 
called  Analytical  (from  the  Greek  word  ai/aXvo-t?),  because 
it  may  be  regarded  as  the  breaking  up  of  a  whole  into  its 
parts,  the  resolution  of  the  final  conclusion  of  a  series 
of  syllogisms  into  the  various  premisses  on  which  it  de- 
pends, and  of  which  it  is,  as  it  were,  the  total  expression. 
The  latter  method  is  called  Synthetical  (from  the  Greek 
word  (rvv6€ais),  because  it  may  be  regarded  as  the  putting 
together  of  the  parts  into  a  whole,  the  combination  of  the 
various  premisses  into  a  conclusion  which  is,  as  it  were, 
their  total  result.  The  Synthetical  Method  is  also 
sometimes  called  Progressive,  and  the  Analytical  Method 
Regressive,  for  reasons  which  will  be  apparent  from  what 
has  already  been  said. 

The  words  a  priori  and  a  posteriori  may  also  be  used 
to  express  the  same  distinction.  In  inductive  inference 
(to  which  these  terms  are  more  properly  applied)  we  are 
said  to  proceed  a  posteriori,  when,  a  certain  event  having 
taken  place,  we  attempt  to  trace  the  steps  by  which  it 
came  about,  or,  a  certain  phenomenon  being  presented 
to  us  for  examination,  we  attempt  to  infer  the  mode  of 
its  production;  and,  vice  versa,  we  are  said  to  proceed 
a  priori,  when,  from  our  knowledge  of  certain  circum- 
stances, we  attempt  to  predict  an  event,  or,  by  putting  in 


158  METHOD  AS  APPLIED  TO  THE  ARRANGEMENT 

operation  certain  causes,  we  attempt  to  discover  their  effect. 
Similarly,  in  deductive  inference,  if,  a  conclusion  being 
assumed  as  provisionally  true,  we  attempt  to  discover 
reasons  for  it,  we  may  be  said  to  proceed  a  posteriori ;  if, 
starting  with  the  premisses,  we  go  on  combining  them  to 
see  whither  they  will  lead  us,  we  may  be  said  to  proceed  a 
priori.  In  the  former  method  of  reasoning,  we  are  pecu- 
liarly liable  to  impose  on  ourselves  or  others  by  availing 
ourselves  of  premisses  which  are  fanciful,  obscure,  in- 
capable of  proof,  questionable,  or  untrue,  especially  if  the 
conclusion  express  some  cherished  conviction  or  some 
position  which  it  is  the  interest  of  ourselves,  our  class, 
or  our  party  to  accept  and  to  disseminate.  Whenever, 
therefore,  we  argue  from  our  conclusions  backwards, 
especial  caution  is  required,  if  it  be  our  sincere  desire  to 
test  our  convictions  impartially. 

There  is  also  a  more  general  employment  of  these 
latter  expressions,  according  to  which  the  term  a  posteriori 
is  appropriated  to  designate  inductive  reasoning,  which 
ought  always  to  be  based  on  individual  facts  of  observa- 
tion ;  a  priori  to  designate  deductive  reasoning,  which 
proceeds  from  general  principles.  The  expression  a  priori 
is  often  applied  by  way  of  censure  to  deductive  reasoning, 
when  the  general  principles  from  which  it  proceeds  are 
supposed  to  rest  on  no  ultimate  inductions  from  fact,  but 
to  be  mere  assumptions  arbitrarily  taken  for  granted  by 
the  author  who  employs  them. 


OF  SYLLOGISMS  IN  A  TRAIN  OF  REASONING.    159 

Note, — For  an  account  of  the  various  senses  in  which 
the  words  *  analysis'  and  *  synthesis'  are  or  have  been 
employed,  the  student  is  referred  to  Sir  W.  Hamilton's 
Lectures  on  Logic,  Lect.  xxiv,  and  Dr.  Hansel's  edition 
of  Aldrichy  Appendix  G. 


fi 


11'' 


I 


APPENDIX. 

On  the  Five  Words  '  Genus ^  'Species^ 
'Differential  'Property I  'Accident! 

WHEN  two  classes  are  so  related  to  each  other  that  one 
is  contained  under  the  other,  the  larger  or  containing  class  is 
called  the  Genus^  and  the  smaller  or  contained  class  is  called 
the  Species.  Thus,  if  we  compare  animal  and  man,  man  is 
a  species,  and  animal  the  genus  ;  if  a  man  and  Englishman, 
man  is  the  genus,  and  Englishman  a  species  :  if  we  compare 
moss-rose  and  rose,  moss-rose  is  a  species,  and  rose  the 
genus  ;  if  rose  and  flower,  flower  is  the  genus,  and  rose  a 
species. 

Genera  and  Species  are  denoted  by  Common  Terms,  which 
themselves  also,  as  well  as  the  groups  which  they  denote, 
are  called  Genera  and  Species. 

In  the  A  proposition,  a  genus  can  be  predicated  of  a 
species,  but  not  a  species  of  a  genus.  Thus  we  can  say 
*  All  men  are  animals,'  or  *  Man  is  an  animal,'  but  not  *  All 
animals  are  men,'  or  *  An  animal  is  a  man.*  In  the  I  pro- 
position, on  the  other  hand,  the  genus  may  be  the  subject, 
and  in  the  O  proposition,  if  the  terms  compared  are  genus 
and  species,  must  be. 

The  distinction  between  Differentia,  Property,  and  Acci- 
dent is  more  difficult,  but  may  be  explained  by  reference 
to  what  has  been  said  (Pt.  I.  ch.  ii.)  on  the  Connotation 
of  Terms. 

As  the  former  distinction  was  applicable  to  classes  and  the 
common  terms  which  denote  them,  so  this  is  applicable  to 


APPENDIX. 


i6i 


attributes  and  the  attributives  by  which  attributes  are  ex- 
pressed. It  may  be  noticed  also  that  a  Differentia,  Property, 
or  Accident,  being  expressed  by  an  Attributive,  must  be 
a  predicate  and  cannot  be  a  subject.  Now,  taking  any 
common  term,  or  any  abstract  term  used  as  a  common 
term,  like  triangle,  an  attributive  predicated  of  it  may  ex- 
press either  part  of  its  connotation  or  not.  Thus,  if  we 
assert  that  ^  A  triangle  is  a  three-sided  rectilineal  figure,*  the 
term  *  three-sided,'  like  the  genus  ^  figure,'  is  connoted  by  the 
very  term  *  triangle.'  Moreover,  the  term  *  three-sided ' 
serves  to  differentiate  or  distinguish  *  triangle '  from  all  other 
rectilineal  figures,  such  as  quadrilateral,  pentagon,  &c.  Hence 
we  may  define  differentia  as  on  p.  45.  Here  however  a 
difficulty  occurs.  Two  or  more  species  falling  under  the 
same  genus  may  be  distinguished  by  more  than  one  dif- 
ferencing attribute.  In  this  case  we  should  speak  of  the 
differentice,  or  we  might  speak  of  the  differentia  as  the  sum 
of  the  differeniice. 

But,  in  case  the  attributive  does  not  express  any  part  of  the 
connotation  of  the  term,  it  may,  nevertheless,  express  some 
attribute  which  foUows  from  the  connotation.  Thus,  if  we 
say  *  A  triangle  is  a  rectilineal  figure  having  the  sum  of  its 
angles  equal  to  two  right  angles,'  we  are  predicating  by  the 
expression  *  having '  &c.,  not  part  of  the  connotation  of 
the  word  triangle,  but  an  attribute  which  nvay  be  directly 
inferred  from  part  of  the  connotation.  Or,  again,  if  we  were 
dealing  with  some  moral  or  physical  phenomenon,  the  attri- 
bute might  follow,  not  as  a  conclusion  from  a  premiss,  but  as 
an  effect  from  a  cause.  Thus  we  might  predicate  of  man  that 
he  is  *  capable  of  progress,'  this  capability  being  regarded  as 
an  effect  of  his  rationality ;  or  of  animal  and  vegetable  tissues 
that  they  are  liable  to  decay,  this  liability  being  regarded 
as  an  effect  of  the  material  of  which  they  are  composed 
and  the  influences  to  which  they  are  subject.  Hence  the 
definition  oi  Property  on  p.  45. 

M 


y 


tfi 


i 


\\ 


i62 


APPENDIX, 


Lastly,  the  attributive  may  neither  express  any  part  of 
the  connotation  of  the  term,  nor  any  attribute  which  follows 
from  part  of  the  connotation.  In  this  case  it  is  called  an 
Accident.  But  accidents  are  of  two  kinds.  If  an  accident  may 
be  predicated  of  all  the  individuals  denoted  by  a  common 
term,  as,  to  take  the  conventional  instance,  blackness  of  crows, 
it  is  called  an  Inseparable  Accident.  In  the  most  common 
case,  where  it  is  predicable  of  some  of  the  individuals  and 
not  of  others,  as,  for  instance,  blackness  of  men,  it  is  called 
a  Separable  Accident. 

The  student  is  recommended  to  compare,  throughout,  this 
explanation  with  the  definitions  given  on  p.  45. 


EXAMPLES. 


^1 


# 


c-cNS»<5S$3fic9''e>*S)o-» 


^'i 


M  2 


EXAMPLES. 

EXAMINE  the  following  Definitions  or  Descriptions 
(pointing  out  their  faults,  if  any,  and,  where  they 
are  sufficient,  stating  under  what  head  of  Defini- 
tion or  Description  they  fall). 

( 1 )  A  square  is  a  four-sided  rectilinear  figure,  having  all  its 

sides  equal. 

(2)  Monarchy  is  a  form  of  political  government  in  which 

one  man  is  sovereign. 

(3)  An  University  is  a  corporation  which  grants  learned 

degrees. 

(4)  Logic  is  the  Art  of  Reasoning. 

(5)  A  plane  triangle  is  a  figure  generated  by  the  section  of 

a  cone  passing  through  the  vertex  and  perpendicular 
to  the  base. 

(6)  Wealtli  is  the  sum  of  things  useful,  necessary,  and 

agreeable. 

(7)  Man  is  a  mammal  having  hands  and  cooking  his  own 

food. 

(8)  An  animal  is  a  sentient  organised  being. 

(9)  A  liquid  is  that  which  can  be  poured  out. 

(10)  A  Federation  is  a  political  union  the  members  of  which 

are  bound  together  for  purposes  of  offence  and  de- 
fence. 

(11)  Man  is  a  mammal  possessing  the  power  of  articulate 

speech. 

(12)  Political  Philosophy  is  the  science  of  the  laws  which 

govern  the  equilibrium  and  development  of  human 
society. 


.  ll 


1 66 


EXAMPLES, 


Examine  the  following  Divisions,  substituting,  where  they 
are  incorrect,  one  or  more  correct  ones. 

(i)  Men  into  Aryans,  Mongolians,  Africans,  and  Americans. 

(2)  Quadrilateral  Figures  into  Squares,  Rectangles,  Paral- 
lelograms, and  Rhomboids. 
^     (3)  The    Fine    Arts   into    Painting,    Drawing,    Sculpture, 
Architecture,  Poetry,  and  Photography. 

(4)  Governments  into  Monarchies,  Tyrannies,  Oligarchies, 

and  Democracies. 

(5)  Books  into  entertaining  and  unentertaining. 

(6)  Men  into  those  who  lend  and  those  who  borrow. 

(7)  The  Sciences  into  Physical,  Social,  Ethical,  Logical,  and 

Metaphysical. 

(8)  Plants  into  Flowering  Plants,  Mosses,  Ferns,  and  Pines. 

(9)  The  origin  of  Colonies    is  to  be  traced  either  to  the 

necessity  for  frontier  garrisons  (as  amongst  the 
Romans)  or  to  the  poverty  or  discontent  of  the 
inhabitants  of  the  mother- country  (as  amongst  the 
Greeks  and  ourselves). 
(10)  *The  general  stock  of  any  country  or  society  is  the 
same  with  that  of  all  its  inhabitants  or  members, 
and  therefore  naturally  divides  itself  into  the  same 
three  portions,  each  of  which  has  a  distinct  function 
or  office : 

1st,  that  portion  which  is  reserved  for  immediate  con- 
sumption, and  of  which  the  characteristic  is  that 
it  affords  no  revenue  or  profit  ; 

2nd,  the  fixed  capital,  of  which  the  characteristic  is  that 
it  affords  a  revenue  or  profit  without  circulating  or 
changing  masters  ; 

3rd,  the  circulating  capital,  of  which  the  characteristic 
is  that  it  affords  a  revenue  only  by  circulating  or 
changing  masters.'— Adam  Smith's  IVea/^k  of  Nations, 
Vol.  ii.  ch.  i. 


EXAMPLES, 


167 


Convert  the  following  propositions  (previously  permuting 

them,  where  necessary). 


(I 
(2 
(3 

(4 

(5 
(6 

(7 

(8 

(9 

(10: 

(II 

(12 

(13 
(14 
(15 
(16 

(17 


All  plane  triangles  are  rectilinear  figures. 

All  plane  triangles  are  three-sided  rectilinear  figures.   ^^ 

All  plane  triangles  may  be  defined  as  three-sided  rec- 
tilinear figures. 

Some  branches  of  Mathematics  admit  of  a  direct  prac- 
tical application. 

Men  of  fair  promises  are  often  not  to  be  trusted. 

Some  members  of  the  Government  are  not  prepared  to 
accept  the  measure. 

Virtue  is  a  condition  of  Happiness. 

Virtue  is  the  condition  of  Happiness. 

A  syllogism  is  a  form  of  inference.  y<^ 

With  man  many  things  are  impossible.  ^  A  \\  ^ 

Some  men  of  great  powers  of  imagination  are  not  poets.  Cvwx,^  U« 

None  but  persons  of  great  powers  of  imagination  are 
poets. 

What  I  have  written,  I  have  written. 

Propositions  are  either  simple  or  complex. 

The  proper  study  of  mankind  is  man. 

Only  the  ignorant  affect  to  despise  knowledge. 

He  can't  be  wrong  whose  life  is  in  the  right. 


ft 


State  in  logical  form  (where  necessary)  and  examine  the 

following  arguments. 

(i)  Every  book  is  liable  to  error, 

Every  book  is  a  human  production ; 
.'.  All  human  productions  are  liable  to  error. 

(2)  All  tulips  are  beautiful  flowers, 
No  roses  are  tulips  ; 
.*.  No  roses  are  beautiful  flowers. 


i68 


EXAMPLES, 


(3)  Some  men  are  wise, 
Some  men  are  good ; 

.*.  Some  wise  men  are  good. 

(4)  All  wise  men  are  good, 
Socrates  was  a  wise  man  ; 

.'.  He  was  good. 

(5)  Some  mathematicians  are  logicians, 

No    logicians    are    unacquainted    with    the    works   of 
Aristotle ; 

/.Some  mathematicians  are  not  unacquainted  with  the 
works  of  Aristotle. 

(6)  No  persons  destitute  of  imagination  are  true  poets, 
Some    persons   destitute    of    imagination     are    good 

logicians ; 
/.^Some  good  logicians  are  not  true  poets. 

(7)  No  persons  destitute  of  imagination  are  true  poets. 
Some    persons    destitute    of    imagination    are    good 

logicians ;  « 

.*.  Some  true  poets  are  not  good  logicians. 

(8)  If  Caesar  was  a  tyrant,  he  deserved  to  die, 
Caesar  was  not  a  tyrant ; 

.'.  He  did  not  deserve  to  die. 

(9)  If  virtue  is  involuntary,  vice  is  also  involuntary. 
Vice  is  voluntary ; 

.*.  Virtue  is  also  voluntary. 

(10)  All  valid  syllogisms  have  three  terms. 
This  syllogism  has  three  terms  ; 
.*.  It  is  a  valid  syllogism. 

(ii)  Some  learned  men  have  become  mad. 
He  is  not  a  learned  man  ; 
.*.  He  will  not  become  mad. 

(12)  The    Reformers    were    bitter   enemies    of  the    Papal 
Supremacy, 


EXAMPLES, 


169 


A  B  was  a  Reformer  (for  he  was  prominent  in  sup- 
porting the  Reform  Bill  of  1832)  ; 
.*.  He  was  a  bitter  enemy  of  the  Papal  Supremacy. 

(13)  Logic  is  either  a  science  or  an  art. 
It  is  a  science ; 

.'.  It  is  not  an  art. 

(14)  Six  and  seven  are  even  and  uneven. 
Thirteen  is  six  and  seven ; 

.*.  Thirteen  is  even  and  uneven. 

(15)  He  must  be  a  Mahommedan,  for  only  Mahommedans 

hold  these  opinions. 

(16)  He  must  be  a  Mahommedan,  for  all   Mahommedans 

hold  these  opinions. 

(17)  To  reject   this   proposal  would  be  unreasonable,  and 

consequently  to  accept  it  is  reasonable. 

(18)  This   event    happened    either    at    Rome,    Naples,    or 

Florence;  it  did  not  happen  at  Rome  or  Naples, 
and  consequently  it  must  have  happened  at 
Florence. 

(19)  Logic  is  indeed  worthy  of  being  cultivated,  if  Aristotle 

is  to  be  regarded  as  infallible  ;  but  he  is  not :  Logic 
therefore  is  not  worthy  of  being  cultivated. 

(20)  An  indissoluble  association  of  ideas  conHnands  belief, 

and  consequently  every  belief  is  the  consequence  of 
an  indissoluble  association  of  ideas. 

(21)  This  measure    would  be    destructive  of  the  national 

prosperity,  and  I  cannot  adduce  a  more  cogent 
argument  than  that,  five  years  ago,  you  were  your- 
self of  the  same  opinion. 

(22)  If  a  man  cannot  make  progress  towards  perfection,  he 

must  either  be  a  brute  or  a  divinity ;  but  no  man  is 
either:  therefore  every  man  is  capable  of  such  progress. 

(23)  Lias  lies  above  New  Red  Sandstone,  New  Red  Sand- 


III 


170 


EXAMPLES, 


stone  lies  above  coal ;  therefore  Lias  lies  above 
Coal. 

(24)  My  hand  touches  the  pen  ;  the  pen  touches  the  paper  : 

therefore  my  hand  touches  the  paper. 

(25)  A,  B,  C,  D,  and  E,  are  the  only  German  students  I 

know :  they  are  all  men  of  considerable  intellectual 
attainments,  and  consequently  I  may  infer  that  all 
German  students  are  men  of  considerable  intellec- 
tual attainments. 

(26)  All  equilateral  triangles  are  equiangular,  and  therefore 

all  equiangular  triangles  must  be  equilateral. 

(27)  These  two  figures  are  equal  to  the  same  figure,  and 

therefore  to  one  another. 

(28)  For  those  who  are  bent  on  cultivating  their  minds  by 

diligent  study,  the  incitement  of  academical  honours 
is  unnecessary ;  and  it  is  ineffectual  for  the  idle  and 
such  as  are  indifferent  to  mental  improvement : 
therefore  the  incitement  of  academical  honours  is 
either  unnecessary  or  ineffectual. 

(29)  He  has  no  appreciation  of  beauty,  for  he  has  no  taste 

for  Pictures. 

(30)  Warm  countries  alone  produce  wines,  Spain  is  a  warm 

country  ;  therefore  Spain  produces  wines. 

(31)  The  Germans  are  a  literary  nation ;    therefore  A  B, 

who  is  a  German,  is  a  literary  man. 

(32)  We  must  increase  the  income-tax,  for  war  has  become 

a  necessity,  and  we  cannot  go  to  war  without  money, 
and  money  can  only  be  raised  by  taxation,  and  the 
only  tax  which  the  resources  of  the  country  can  bear 
is  the  income-tax,  which  will  fall  on  the  richer  part 
of  the  population. 

(33)  Governors  of  dependencies  should  be  vested  with  ab- 

solute power,  for  otherwise  it  is  impossible  to  crush 
rebellion. 


EXAMPLES. 


171 


(34)  A  is  larger  than  B,  and  B  is  larger  than  C  ;  therefore, 

a  fortiori,  A  is  larger  than  C. 

(35)  Alexander  is  the  son  of  Philip,  and  therefore  Philip  is 

the  father  of  Alexander. 

(36)  If  *  to  improve  is  to  change,  and  to  be  perfect  is  to 

have  changed  often,'  what  hope  can  we  entertain  of 
those  who  oppose  change  ? 

(37)  Luxury  is  at  once  beneficial  and  injurious  to  society; 

for  luxury  is  the  using  the  gifts  of  Providence,  either 
to  the  injury  of  the  user,  or  to  the  injury  of  others 
towards  whom  the  user  stands  in  any  relation  which 
obliges  him  to  aid  and  assistance ;  but  luxury  causes 
expenditure  of  money,  and  therefore  is  beneficial  to 
society. 

(38)  Old  age   is    wiser   than    youth ;    therefore   it   is   only 

reasonable  that  we  should  be  guided  by  the  de- 
cisions of  our  ancestors. 

(39)  A  man  cannot  always  be  right   in  his  opinions,  and 

therefore  we  ought  continually  to  distrust  our 
judgments. 

(40)  Had  an  armistice  been  beneficial  to  France  and  Ger- 

many, it  would  have  been  agreed  upon  by  those 
powers  ;  but  such  has  not  been  the  case :  it  is 
plain,  therefore,  that  an  armistice  would  not  have 
been  advantageous  to  either  of  the  bellfgerents. 

(41)  If  education   is   popular,  compulsion   is   unnecessary ; 

if  unpopular,  compulsion  will  not  be  tolerated. 

(42)  I  will  not  do  this  act,  because  it  is  unjust  ;  I  know 

that  it  is  unjust,  because  my  conscience  tells  me  so, 
and  my  conscience  tells  me  so,  because  the  act  is 
wrong. 

(43)  This  proposition  is  too  good  to  be  practicable. 

(44)  Such  and  such  a  system  of  education   has   produced 

several  distinguished  men  ;  therefore  it  does  not 
admit  of  any  improvement. 


iT% 


EXAMPLES. 


EXAMPLES, 


173 


(45)  Slavery  is  a  natural  institution  ;  but  what  is  natural  is 

just,  and  what  is  just  it  is  unjust  to  abrogate ;  and 
consequently  it  would  be  unjust  to  abrogate  slavery. 

(46)  *  Mercy  but  murders,  pardoning  those  that  kill.* 

Romeo  and  Juliet^  Act  iii.  Sc.  i. 

(47)  A,  B,  and  C  have  distinguished  themselves  both  in 

athletic  sports  and  intellectual  pursuits;  therefore 
those  who  are  most  famous  for  their  excellence  in 
athletic  sports  are  generally  most  famous  for  their 
intellectual  attainments  as  well. 

(48)  What  is  called  a  *  constitutional  monarchy'  is  impos- 

sible, for  the  sovereign  authority  of  a  state  cannot 
be  limited  by  law ;  now  the  king  is  sovereign,  and, 
as  such,  cannot  be  subject  to  any  superior  authority. 

(49)  Parallel  lines  are  equi-distant  ;   for,  if  from  two  points 

in  one  of  them  perpendiculars  be  drawn  to  the 
other,  these  perpendiculars  are  parallel  (Euc.  I.  28), 
and  the  two  lines  intercepted  between  them  are 
parallel ;  therefore  a  parallelogram  is  formed,  of 
which  the  perpendiculars  are  opposite  sides  and 
therefore  equal. 

(50)  If  Bacon's  opinion  is  right,  it  is  improper  to  stock  a 

new  colony  with  the  refuse  of  jails :  but  this  course  we 
must  allow  not  to  be  improper,  if  our  method  of 
colonising  New  South  Wales  be  a  wise  one  :  if  this 
be  wise,  therefore.  Bacon's  opinion  is  not  right. 

(51)  *  Profit'  is  interpreted  in.  the  dictionary  *  advantage'; 

to  take  profit,  then,  is  to  take  advantage  :  it  is 
wrong  to  take  advantage  of  one's  neighbour :  there- 
fore it  is  wrong  to  take  profit. 

(52)  Romulus  must  be  a  historical  person,  because  it  is  not 

at  all  likely  that  the  Romans,  whose  memory  was 
only  burdened  with  seven  kings,  should  have  for- 
gotten the  most  famous  of  them,  namely,  the  first. 

(53)  You  maintain  that  an  action  can  only  be  called  virtuous, 


if  it  contribute  to  the  welfare  of  mankind  or  of  some 
section  of  mankind :  hence  you  are  botftid  to  regard 
every  convenient  object,  for  instance  a  horse,  a  tree, 
or  a  chair,  as  virtuous. 

(54)  The  knowledge  of  things  is  more  useful  than  the  know- 

ledge of  words  ;  and,  therefore,  the  study  of  nature 
is  more  improving  to  the  mind  than  the  study  of 
language. 

(55)  In  a  lottery  it  is  improbable  that  any  particular  ticket- 

holder  will  draw  the  prize.  But  some  one  must  draw 
the  prize.  Therefore  something  improbable  must 
happen. 

(56)  My  informant  A  heard  his  story  from  B,  who  would 

certainly  tell  it  as  originally  told  to  him  ;  B  heard  it 
from  C,  who  would  probably  tell  it  accurately ; 
C  from  D,  who  would  also  probably  tell  it  accurately ; 
D  from  E,  who,  I  have  no  reason  to  suppose,  would 
tell  it  inaccurately :  I  may  consequently  receive  A's 
story  as  probably  accurate. 

(57)  Large  colonies  are  as  detrimental  to  the  power  of  a 

state  as  overgrown  limbs  to  the  vigour  of  the  human 
•    body. 

(58)  All  law  is  an  abridgment  of  liberty,  and  consequently 

of  happiness. 

(59)  I  am  under  an  obligation  to  do  it,  but  he  Who  is  obliged 

has  no  power  of  resistance ;  consequently  I  have  no 
choice  about  the  matter. 

(60)  You  never  give  an  opinion  without  believing  yourself 

to  be  right,  and  therefore  you  must  suppose  yourself 
to  be  infallible. 

(61)  If  man  be  not  a  necessary  agent,  determined  by  plea- 

sure and  pain,  there  is  no  foundation  for  rewards  and 
punishments.  These  would  be  useless,  unless  men 
were  necessary  agents,  and  were  determined  by 
pleasure  and  pain:   because,  if  men  were  free  and 


li^' 


I 


174 


EXAMPLES. 


EXAMPLES. 


175 


indifferent  to  pleasure  and  pain,  pain  could  be  no 
motive  to  cause  men  to  observe  the  law. 

(62)  Night  invariably  precedes  day,  and  therefore  night  must 

be  the  cause  of  day. 

(63)  The  planet  Mars  resembles  the  Earth  in  the  possession  of 

an  atmosphere,  clouds,  and  water,  and  has  a  tempera- 
ture in  which  terrestrial  life  might  exist,  and,  therefore, 
it  is  probably  inhabited  as  the  earth  is. 

(64)  *  If  it  be  fated  that  you  recover  from  your  present  dis- 

ease, you  will  recover,  whether  you  call  in  a  doctor 
or  not ;  again,  if  it  be  fated  that  you  do  not  re- 
cover from  your  present  disease,  you  will  not  recover, 
whether  you  call  in  a  doctor  or  not :  but  one  or  other 
of  these  contradictories  is  fated,  and  therefore  it  can 
be  of  no  service  to  call  in  a  doctor.*— {/^nava  Ratio.) 

(65)  The  story  of  the  formation  of  the  human  race  by  Prome- 

theus must  be  true,  for  the  clay  from  which  he  formed 
it  was  shown  in  Greece  within  historical  times. 

(66)  The  Latin  word  *  virtus '  originally  meant  *  manliness  * ; 

hence  the  virtue  of  manliness  or  courage  is  the  highest 
virtue  and  the  type  of  all  other  virtues. 

(67)  This  person  may  reasonably  be  supposed  to  have  com- 

mitted the  theft,  for  he  can  give  no  satisfactory  ac- 
count of  himself  on  the  night  of  the  alleged  offence ; 
moreover  he  is  a  person  of  bad  character,  and,  being 
poor,  is  naturally  liable  to  a  temptation  to  steal. 

(68)  Opium  produces  sleep,  for  it  possesses  a  soporific  virtue. 

(69)  The  student  of  History  is  compelled  to  admit  the  truth 

of  the  Law  of  Progress,  for  he  finds  that  Society  has 
never  stood  still. 

(70)  You  are   inconsistent  with  yourself,  for  you   told   me 

yesterday  that  there  was  a  presumption  of  this  man's 
guilt,  and  now,  when  I  say  that  I  may  presume  his 
guilt,  you  contradict  me. 
71)  'Suppose  one  man  should  by  fraud  or  violence  take  from 


another  the  fruit  of  his  labour  with  intent  to  give  it  to 
a  third,  who,  he  thought,  would  have  as  much  pleasure 
from  it  as  would  balance  the  pleasures  which  the  first 
possessor  would  have  had  in  the  enjoyment  and  his 
vexation  in  the  loss  of  it ;  suppose  also  that  no  bad  con- 
sequences would  follow;  yet  such  an  action  would 
surely  be  vicious.'     Butler,  On  the  Nature  of  Virtue. 

(72)  There  exist  many   differences   of   opinion   and   much 

uncertainty  with  regard  to  many  questions  connected 
with  Geology  ;  consequently  Geology  is  not  a  science, 
and  any  arguments  which  assume  the  truth  of  geo- 
logical theories  must  invariably  be  regarded  with 
considerable  suspicion. 

(73)  *  Suppose  Achilles  to  move  ten  times  as  fast  as  the 

Tortoise,  but  the  Tortoise  to  have  the  start  of 
Achilles,  say,  by  one-tenth  of  the  distance  to  be 
traversed:  when  Achilles  has  arrived  at  the  point 
from  which  the  Tortoise  started,  the  Tortoise  will 
still  be  one-hundredth  part  of  the  whole  distance  in 
advance  of  him ;  when  Achilles  has  reached  this  point, 
the  Tortoise  will  still  be  one-thousandth  part  of  the 
whole  distance  in  advance  of  him ;  and  so  on.  Thus 
Achilles  will  never  be  able  to  pass  the  Tortoise.' 

{Fallacy  of  Achilles  and  the  Tortoise) 

(74)  *  Epimenides  the  Cretan  says  that  "  all  the  Cretans  are 

liars,"  but  Epimenides  is  himself  a  Cretan  ;  therefore 
he  is  himself  a  liar.  But  if  he  be  a  liar,  what  he 
says  is  untrue,  and  consequently  the  Cretans  are 
veracious  ;  but  Epimenides  is  a  Cretan,  and  there- 
fore what  he  says  is  true ;  hence  the  Cretans  are 
liars,  Epimenides  is  himself  a  liar,  and  what  he  says 
is  untrue.  Thus  we  may  go  on  alternately  proving 
that  Epimenides  and  the  Cretans  are  truthful  and 
untruthful.' — {Fallacy  of  Mentiens.) 

(75)  The  idea  of  the  obligation  to  virtue  is  innate,  for  it  is 


176 


EXAMPLES, 


EXAMPLES, 


177 


found  in  all  men,  and  it  could  not  be  universal  if  it 

were  acquired  by  experience. 
(76)  Berkeley's  Theory  of  the   Non-existence  of  Matter  is 

palpably  absurd,  for  it  is  impossible  even  to  place 

one's  foot  on  the  ground  without  experiencing  the 

resistance  of  matter. 
{']^')  I  have  no  hesitation  in  saying  that  the  proposition, 

however  good  in  theory,  is  in  practice  utterly  absurd. 

(78)  If  any  objection  that  can  be  urged  would  justify  a  change 

of  established  laws,  no  laws  could  reasonably  be  main- 
tained ;  but  some  laws  can  reasonably  be  maintained : 
therefore  no  objection  that  can  be  urged  will  justify 
a  change  of  established  laws. 

(79)  I  cannot  accept  your  opinion  as  true,  for  it  seems  to  me 

that  its  general  recognition  would  be  attended  with 
the  most  injurious  consequences  to  society. 

(80)  Why    should    any  but    professional  moralists   trouble 

themselves  with  the  solution  of  moral  difficulties  ? 
For,  as  we  resort  to  a  physician  in  case  of  any 
physical  disease,  so,  in  the  case  of  any  moral  doubt 
or  any  moral  disorganisation,  it  seems  natural  that 
we  should  rely  on  the  judgment  of  some  man  spe- 
cially skilled  in  the  treatment  of  such  subjects. 

(81)  *Wood,  stones,  fire,  water,  flesh,  iron,  and  the  like  things, 

which  I  name  and  discourse  of,  are  things  that  I  know. 
And  I  should  not  have  known  them  but  that  I  per- 
ceived them  bymy  senses ;  and  things  perceived  by  the 
senses  are  immediately  perceived ;  and  things  imme- 
diately perceived  are  ideas ;  and  ideas  cannot  exist 
without  the  mind ;  their  existence  therefore  consists 
in  being  perceived  ;  when,  therefore,  they  are  actually 
perceived  there  can  be  no  doubt  of  their  existence.' 
Berkeley,  Third  Dialogue  between  Hy las  andPhilonous, 

(82)  *And  because  the  greatest  part  of  men  are  such  as 

prefer  their  own  private  good  before  all  things,  even 


that  good  which  is  sensual  before  whatsoever  is  most 
divine  ;  and  for  that  the  labour  of  doing  good,  toge- 
ther with  the  pleasure  arising  from  the  contrary, 
doth  make  men  for  the  most  part  slower  to  the  one 
and  proner  to  the  other,  than  that  duty  prescribed 
them  by  law  can  prevail  sufficiently  with  them  :  there- 
fore unto  laws  that  men  do  make  for  the  benefit  of  men 
it  hath  seemed  always  needful  to  add  rewards,  which 
may  more  allure  unto  good  than  any  hardness  deter- 
reth  from  it,  and  punishments,  which  may  more  deter 
from  evil  than  any  sweetness  thereto  allureth.' 

Hooker,  Reel,  Pol.  Bk.  I.  x.  (6.) 

(83)  '  The  scarcity  of  a  dear  year,  by  diminishing  the  de- 

mand for  labour,  tends  to  lower  its  price,  as  the  high 
price  of  provisions  tends  to  raise  it.  The  plenty  of 
a  cheap  year,  on  the  contrary,  by  increasing  the 
demand,  tends  to  raise  the  price  of  labour,  as  the 
cheapness  of  provisions  tends  to  lower  it.  In  the 
ordinary  variations  of  the  price  of  provisions,  those 
two  opposite  causes  seem  to  counterbalance  one 
another;  which  is  probably  in  part  the  reason  why 
the  wages  of  labour  are  everywhere  so  much  more 
steady  and  permanent  than  the  price  of  provisions.' 
Adam  Smith,  Wealth  of  Nations^  Bk.  I.  ch.  viii. 

(84)  *  I  am  a  Jew.     Hath  not  a  Jew  eyes?   hath" not  a  Jew 

hands,  organs,  dimensions,  senses,  affections,  passions? 
fed  with  the  same  food,  hurt  with  the  same  weapons, 
subject  to  the  same  diseases,  healed  by  the  same 
means,  warmed  and  cooled  by  the  same  winter  and 
summer,  as  a  Christian  is  ?  If  you  prick  us,  do  we 
not  bleed  ?  If  you  tickle  us,  do  we  not  laugh  ?  If  you 
poison  us,  do  we  not  die  ?  and  if  you  wrong  us,  shall 
we  not  revenge  ?  If  we  are  like  you  in  the  rest,  we 
will  resemble  you  in  that.' 

Merchant  of  Venice,  Act  iii.  Sc.  I. 

N 


;?   t 


k 


^'  W 


178 


EXAMPLES, 


EXAMPLES. 


J79 


(85)  *  The  most  striking  and  important  of  the  effects  of  heat 

consist,  however,  in  the  liquefaction  of  soHd  substances, 
and  the  conversion  of  the  liquids  so  produced  into 
vapour.  There  is  no  solid  substance  known  which, 
by  a  sufficiently  intense  heat,  may  not  be  melted,  and 
finally  dissipated  in  vapour ;  and  this  analogy  is  so 
extensive  and  cogent,  that  we  cannot  but  suppose  that 
all  those  bodies  which  are  liquid  under  ordinary  cir- 
cumstances, owe  their  liquidity  to  heat,  and  would 
freeze  or  become  solid  if  their  heat  could  be  suffi- 
ciently reduced.  In  many  we  see  this  to  be  the  case 
in  ordinary  winters ;  for  some,  severe  frosts  are  requi- 
site ;  others  freeze  only  with  the  most  intense  arti- 
ficial colds ;  and  some  have  hitherto  resisted  all  our 
endeavours  ;  yet  the  number  of  these  last  is  few,  and 
they  will  probably  cease  to  be  exceptions  as  our  means 
of  producing  cold  become  enlarged.  A  similar  analogy 
leads  us  to  conclude  that  all  aeriform  fluids  are  merely 
liquids  kept  in  the  state  of  vapour  by  heat.  Many  of 
them  have  been  actually  condensed  into  the  liquid 
state  by  cold  accompanied  with  violent  pressure  ;  and 
as  our  means  of  applying  these  causes  of  condensation 
have  improved,  more  and  more  refractory  ones  have 
successively  yielded.  Hence  we  are  fairly  entitled  to 
extend  our  conclusion  to  those  which  we  have  not  yet 
been  able  to  succeed  with ;  and  thus  we  are  led  to 
regard  it  as  a  general  fact,  that  the  liquid  and  aeriform 
or  vaporous  states  are  entirely  dependent  on  heat, 
that  were  it  not  for  this  cause,  there  would  be  nothing 
but  solids  in  nature  ;  and  that,  on  the  other  hand,  no- 
thing but  a  sufficient  intensity  of  heat  is  requisite  to 
destroy  the  cohesion  of  every  substance,  and  reduce 
all  bodies,  first  to  liquids,  and  then  into  vapour.* 
Herschel,  On  the  Study  of  Natural  Philosophy. 

(86)  *  We  are  not  inclined  to  ascribe  much  practical  value  to 


that  analysis  of  the  inductive  method  which  Bacon  has 
given  in  the  second  book  of  the  Novum  Organum.  It 
is  indeed  an  elaborate  and  correct  analysis.  But  it  is 
an  analysis  of  that  which  we  are  all  doing  from  morn- 
ing to  night,  and  which  we  continue  to  do  even  in  our 


dreams.' 


Macaulay,  Essay  on  Bacon, 


(87)  *  Promises  are  not  binding  where  the  performance  is 
unlawful.  There  are  two  cases  of  this  :  one,  where 
the  unlawfulness  is  known  to  the  parties,  at  the  time 
of  making  the  promise ;  as  where  an  assassin  promises 
his  employer  to  despatch  his  rival  or  his  enemy ;  or  a 
servant  to  betray  his  master.  The  parties  in  these 
cases  are  not  obliged  to  perform  what  the  promise 
requires,  because  they  were  under  a  prior  obligation  to 
the  contrary.  From  which  prior  obligation  what  is 
there  to  discharge  them  ?  Their  promise,  their  own 
act  and  deed.  But  an  obligation,  from  which  a  man 
can  discharge  himself  by  his  own  act,  is  no  obligation 
at  all.  The  guilt  therefore  of  such  promises  lies  in 
the  making,  not  in  the  breaking  of  them  ;  and  if,  in 
the  interval  betwixt  the  promise  and  the  performance, 
a  man  so  far  recover  his  reflection,  as  to  repent  of  his 
engagements,  he  ought  certainly  to  break  through 
them.' 

Paley,  Moral  and  Political  Philosophy, 

Bk.  III.  Part  I.  ch.  V. 

(88)  ^This,  I  think,  any  one  may  observe  in  himself,  and 
others,  that  the  greater  visible  Good  does  not  alwaj^s 
raise  men's  desires  in  proportion  to  the  greatness,  it 
appears,  and  is  acknowledged  to  have :  Though  every 
little  Trouble  moves  us,  and  sets  us  on  work  to  get 
rid  of  it.  The  Reason  whereof  is  evident  from  the 
Nature  of  our  Happiness  and  Misery  itself.  All  pre- 
seht  Pain,  whatever  it  be,  makes  a  part  of  our  present 
Misery :  But  all  absent  Good  does  not  at  any  time 

•  N  2 


n 


i8o 


EXAMPLES. 


\ 


make  a  necessary  part  of  our  present  Happiness^  nor 
the  absence  of  it  make  a  part  of  our  Misery.  If  it  did, 
we  should  be  constantly  and  infinitely  miserable ;  there 
being  infinite  degrees  of  Happiness,  which  are  not  in 
cur  possession.  All  Uneasiness  therefore  being  re- 
moved, a  moderate.portion  of  Good  serves  at  present  to 
content  men ;  and  some  few  degrees  of  pleasure  in  a 
succession  of  ordinary  Enjoyments  make  up  a  Happi- 
ness, wherein  they  can  be  satisfied.  If  this  were  not 
so,  there  could  be  no  room  for  those  indifferent,  and 
visibly  trifling  Actions,  to  which  our  Wills  are  so 
often  determined  ;  and  wherein  we  voluntarily  waste 
so  much  of  our  Lives  ;  which  remissness  could  by  no 
means  consist  with  a  constant  determination  of  Will 
or  Desire  to  the  greatest  apparent  Good.* 

Locke,  Essay  concerning  Human  Understandings 
N  Bk.  II.  ch.  xxi.  §  44. 

(89)  '  There  is  only  one  part  of  the  Protectionist  scheme  which 
requires  any  further  notice :  its  policy  towards  colonies, 
and  foreign  dependencies ;  that  of  compelling  them 
to  trade  exclusively  with  the  dominant  country.  A 
country  which  thus  secures  to  itself  an  extra  foreign 
demand  for  its  commodities,  undoubtedly  gives  itself 
some  advantage  in  the  distribution  of  the  general  gains 
of  the  commercial  world.  Since,  however,  it  causes 
the  industry  and  capital  of  the  colony  to  be  diverted 
from  channels,  which  are  proved  to  be  the  most  pro- 
ductive, inasmuch  as  they  are  those  into  which  industry 
and  capital  spontaneously  tend  to  flow ;  there  is  a  loss, 
on  the  whole,  to  the  productive  powers  of  the  world, 
and  the  mother  country  does  not  gain  so  much 
as  she  makes  the  colony  lose.  If,  therefore,  the 
mother  country  refuses  to  acknowledge  any  reciprocity 
of  obligation,  she  imposes  a  tribute  on  the'colony  in 
an  indirect  mode,  greatly  more  oppressive  and  in- 


EXAMPLES, 


181 


jurious  than  the  direct.  But  if,  with  a  more  equitable 
spirit,  she  submits  herself  to  corresponding  restrictions 
for  the  benefit  of  the  colony,  the  result  of  the  whole 
transaction  is  the  ridiculous  one,  that  each  party  loses 
much,  in  order  that  the  other  may  gain  a  little.' 

Mill's  Political  Economy,  Bk.  V.  ch.  x.  §  I. 
(90)  *  The  money  to  replace  what  has  been  burned  will  not 
be  sent  abroad  to  enrich  foreign  manufactures ;  but, 
thanks  to  the  wise  policy  of  protection  which  has 
built  up  American  industries,  it  will  stimulate  our 
own  manufactures,  set  our  mills  running  fasteit,  and 
give  employment  to  thousands  of  idle  workmen. 
Thus  in  a  short  time  our  abundant  natural  resources 
will  restore  what  has  been  lost,  and  in  converting 
the  raw  material  our  manufacturing  interests  will 
take  on  a  new  activity.* 

New  York  Tribune  of  Oct.  24,  1871,  quoted  by 
Professor  Cairnes  in  *  Some  Leading  Prin- 
ciples of  Political  Economy.' 


a-   % 


usually  appears  to  contain  four,  or  perhaps  more,  terms. 
We  must  not,  however,  reject  it  on  that  account,  till  we 
have  previously  attempted  to  translate  the  propositions  of 
which  it  is  composed  into  equivalent  propositions,  con- 
taining among  them  three  terms  only.  The  cases  in 
which  this  cannot  be  done  are  either  those  in  which  the 
terms  of  the  conclusion,  or  at  least  one  of  them,  are 
distinct,  not  in  form  only,  but  in  meaning,  from  any  of 
the  terms  employed  in  the  premisses,  or  those  in  which 
there  is  no  term  common,  or  capable  of  being  repre- 
sented as  common,  to  the  two  premisses.  Thus  the 
syllogism  '  Lias  lies  above  New  Red  Sandstone,  New  Red 


A   syllogism,   when   not   stated   in   logical   form,  i«** 


11 


i82 


EXAMPLES, 


Sandstone  lies  above  Coal;  therefore  Lias  lies  above 
Coal/  obviously  admits  of  being  stated  in  the  form, 
'Whatever  lies  above  New  Red  Sandstone  lies  above 
Coal,  Lias  lies  above  New  Red  Sandstone ;  therefore 
Lias  lies  above  Coal,'  and  consequently  ought  not  to 
be  rejected  as  having  four  terms.  But  the  premisses 
*  Lias  lies  above  New  Red  Sandstone,  the  Cretaceous 
System  lies  above  the  Oolitic,'  contain  no  term  common, 
nor  any  term  capable  (from  a  mere  inspection  of  the 
language)  of  being  represented  as  common,  to  the  pre- 
misses, and  hence  they  might  fairly  be  rejected  as  con- 
taining four  terms,  and  consequently  leading  to  no  con- 
clusion. Even  here,  however,  by  any  one  who  possessed 
sufficient  special  knowledge  of  Geology  to  be  aware  that 
the  Oolitic  System  lies  above  Lias,  the  premisses  might 
be  represented  as  containing  three  terms  only,  and  as 
necessitating  the  conclusion  '  The  Cretaceous  System  lies 
above  New  Red  Sandstone.'  But  from  such  premisses 
as  *Lias  lies  above  New  Red  Sandstone,'  'A  Painting 
should  represent  beauty  of  colour  as  well  as  beauty  of 
form,'  no  conclusion  whatever  could  be  drawn  by  means 
of  either  logical  or  special  knowledge.  The  premisses 
are,  in  fact,  utterly  alien  to  each  other,  or,  in  other  words, 
they  are  not  in  pari  materid.  In  examining  an  argument, 
the  student  may  always  avail  himself  of  any  special  know- 
ledge which  he  may  possess,  provided  that,  in  his  answer, 
he  carefully  distinguish  between  what  is  due  to  such 
special  knowledge  and  what  to  a  knowledge  of  the 
ordinary  usages  of  language  and  of  the  rules  of  Logic. 


EXAMPLES, 


183 


In  the  first  example  given  above,  a  mere  knowledge  of 
the  rules  of  Logic,  without  any  reference  whatever  to  the 
usages  of  language,  would  not  justify  us  in  drawing  any 
conclusion  from  the  premisses ;  the  slightest  acquaintance 
with  the  usages  of  language  would  however  enable  us  to 
represent  the  terms,  which  are  apparently  four,  as  three, 
and  to  infer  the  conclusion  'Lias  lies  above  Coal' 
But  in  the  second  example  no  acquaintance  either 
with  the  rules  of  Logic  or  with  the  ordinary  usages  of 
language  would  enable  us  to  draw  the  conclusion,  '  The 
Cretaceous  System  lies  above  New  Red  Sandstone;' 
such  a  conclusion,  though  valid,  is  only  justified  by  a 
special  knowledge  of  Geology:  no  person,  unacquainted 
with  the  facts  of  Geology,  would  be  justified  in  admitting 
the  conclusion  as  an  inference  from  the  premisses. 

Where  it  is  obvious  that  an  argument  is  intended  to  be 
syllogistic,  and  only  one  premiss  is  stated,  it  is  of  course 
expected  that  the  student  will  supply  the  other  premiss. 

In  some  of  the  examples,  it  may  be  an  useful  exercise 
to  discuss  the  truth  of  the  premisses  as  well  as  the 
legitimacy  of  the  conclusion. 


INDEX. 


Abstract  terms,  p.  1 3. 

—  different  senses  in  which  the 

expression  has  been  employ- 
ed, 15. 

—  sometimes  used  as  common 

terms,  14,  15. 
Accident,  44. 

—  defined,  45. 

—  inseparable,  41,  42. 

—  separable,  42,  43. 
Accidental  propositions,  48. 
Accident  is  fallacia,  1 51-15  3. 
Act,  ambiguity  of  the  word,  4. 

—  or    operation     employed    in 

preference     to     power    or 

faculty,  4. 
'  All,*  ambiguous  use  of  the  word, 

150-151. 
Ambiguous  middle,  87. 

—  terms,   fallacy  of,    87,    141, 

149-155. 
Ampliative  judgments,  48. 

Analogously,  terms  used,  87. 
Analogy,  71,  72. 

—  fallacy  of  false,  140-141. 

—  of  Aristotle,  72,  141. 
Analytical  judgments,  48. 

—  method,  157. 

A  Posteriori  method,  157-158. 
A  Priori  method,  157-158. 
Argument  in  a  circle,  143-145. 


Argumentum  ad  hominem,  148. 

—  ad  populum,  ad  verecundiam, 

&c.,  148. 
Attributives,  13,  14-16. 

—  sometimes  used  as  common 

terms,  14,  15. 

—  when  employed  as  predicates, 

regarded  by  Mr.  Mill  as  com- 
mon terms,  18. 

Begging  the  question,  fallacy  of, 
145- 

Canon  of  reasoning  in  the  first 
figure,  92-94. 

Categorematic  words,  12. 

Categorical  propositions  and  syl- 
logisms, these  expressions 
not  here  employed,  1 1 2-1 13, 

Categories  of  Aristotle,  ix.  66. 

Chain-argument,  109. 

Chain-reasoning,  133. 

Circle,  argument  in  a,  143-145. 

Circumstantial    evidence,     133- 

139- 
Classifications,  65-67. 

—  rules  for,  65-66. 

—  difference    between    Natural 

and  Artificial,  62. 
Collective  terms,  12,  13. 

—  results  of  thought,  1 7, 


i86 


INDEX. 


INDEX. 


187 


Common  terms,  12,  13,  17-18. 
Comparison       (reflexion       or 

thought),  definition  of,  i. 
Composition,  fallacy  of,  149-150. 
Concepts  employed  by  Sir  W. 

Hamilton  in  preference  to 

terms,  8. 
Conclusion,  10,  84. 

—  negative,  96. 

—  particular,  97,  98. 

Concrete  terms,  1 5. 

Conditional  propositions  and  syl- 
logisms, these  expressions 
not  here  employed,  1 1 2-1 1 3. 

Connotation  of  terms,  19-22. 
Contradiction,  law  of,  74,  91. 
Contradictory  terms,  83. 
Contrary  terms,  83. 
Conversion  by  contraposition  or 

negation,  82. 
Conversions,  80-82. 
Copula,  9,  23-27,  128. 
Corroborative    Evidence,    133- 

139- 
Cross-division,  60. 

Cumulative  Evidence,  133-139. 

Definitions,  37,  44,  49-57- 

—  final,  51,  52. 

.  —  incomplete,  52,  53. 

—  provisional,  52,  53. 

—  real  and  nominal,  56,  57. 

—  what  terms  are  incapable  of, 

49- 

—  why  discussed  under  the  se- 

cond part  of  logic,  46. 

—  rules  for  legitimate,  55. 
Denotation  of  terms,  19-22. 


Description  of  a  singular  or  col- 
lective term,  49. 

—  of  a  common  term,  53,  54. 
Designations,  39,  44. 
Dichotomy,  division  by,  61. 
Differentia,  38. 

—  defined,  45. 

—  generic,  64. 

—  specific,  64. 
Differentiae,  50,  51. 

—  difficulty    of    distinguishing 

from  properties,  55,  56. 
Dilemma,  119-123. 
Distinction    distinguished    from 

division,  59. 
Distribution  of  terms,  33-35- 
Divided  term,  58. 
Dividing  members,  58. 
Division,  principle  of,  59-60. 

—  by  dichotomy,  61. 

—  fallacy  of,  149-150. 

—  rules  for  a  legitimate,  62. 

—  what  terms  are    capable  of 

being  divided,  58. 
Divisions,  58-67. 

—  why  discussed  under  the  se- 

cond part  of  logic,  46. 

Enthymeme    of   Aristotle,    86, 

138- 
Enumeration  distinguished  from 

division,  59. 

Epi-syllogism,  109. 

Equivocal  terms,  fallacy  of,  149- 

155- 
Equivocally,  terms  used,  87. 

Essential  propositions,  48. 

Evidence,  cumulative  or  corro- 


borative (including  circum- 
stantial), 133-139- 

Excluded  middle,  law  of,  74,  91. 

Explicative  judgments,  48. 

Extensive  capacity  of  a  term,  21. 

Fallacia  accidentis,  151-153- 

—  a  dicto  simpliciter  ad  dictum 

secundum  quid,  1 51-153.  • 

—  plurium  interrogationum,  155. 
Fallacies,  140-155. 

Fallacy  of  Achilles  and  the  Tor- 
toise, 141,  175. 

—  of  ambiguous    or    equivocal 

terms,   or  of  ambiguity  of 
language,  141,  1 49-155- 

—  of  composition,  149-150. 

—  of  division,  149-150. 

—  of  false  analogy,  140- 141. 

—  of  illicit  process,  95,  143. 

—  of   irrelevancy  or   ignoratio 

elenchi,  147-149. 

—  of  paronymous  terms,    153- 

154- 

—  of  petitio  principii,  144-146. 

—  of  undistributed  middle,  95, 

142-143. 
Figures,  89-90. 

—  are  there  three  or  four?  89-90. 

—  moods  of  the  fourth  may  be  re- 

presented as  indirect  moods 
of  the  first,  io6-io8. 

—  special  rules  of  the,  105. 
Four  terms,  85,  87,  181-183. 
Fundamentum  divisionis,  59-60. 

Genus,  37,  38. 

—  cognate,  64. 


Genus,  defined,  45. 

—  subaltern,  64. 

—  summum,  63,  66. 

Heads  of  predicables,  36-47, 
160-162. 

—  why  discussed  under  the  se- 

cond part  of  logic,  45,  46. 

Identity,  law  of,  74,  91. 
rSioK  of  Aristotle,  37-41,  44. 
Ignoratio  elenchi,  147-149. 
Illicit  process  of  major  or  minor 

term,  95,  143. 
Imagination,  definition  of,  i. 

—  simple  or    reproductive    as 

distinguished  from  complex 
or  productive,  3. 

Import  of  propositions,  46,  47. 

Indefinite  or  indesignate  propo- 
sitions, 29,  30. 

Induction,  sense  in  which  the 
word  is  employed,  68. 

Inductions,  Aristotelian,  75-76. 

—  distinguished  from  deductions, 

69-74. 

—  instances  of,  69-70. 

—  sense  in  which  the  word  is 

employed,  68. 
Inference,  different  senses  of  the 
word,  68. 

—  limitations  of  the  word  by  Sir 

W.  Hamilton  and  Mr.  Mill, 

74-75- 
Inferences,  deductive,  68,  72-75. 

—  defined,  68. 

—  immediate,  68,  73-75,  77-83. 

—  inductive,  68-71,  74-76- 

—  instances  of,  10. 


; 


I  f 


i88 


INDEX, 


INDEX. 


189 


Inferences,  mediate,  68,  73~7^- 

—  various  kinds  of,  68-76. 
Infinitation,  82. 
Inseparable  accident,  41,  42. 
Intensive  capacity  of  a  term,  21. 
Irrelevancy,  fallacy  of,  147-149. 

Judgments,  employed  by  Sir  W. 
Hamilton  in  preference  to 
propositions,  8. 

Language,  its  relation  to  thought, 

7- 
Laws  of  inductive  and  deductive 

reasoning,  74,  91. 

Logic,  definition  of,  5,  6. 

—  its  relation  to  psychology,  3. 

—  Mr.  Mill's  definition  of,  6. 

Major  and  minor  premisses,  85. 
Major  and  minor  terms,  85. 

—  illicit  process  of,  95-96,  143. 

- —  sense  in  which  they  were  em- 
ployed by  Aristotle,  88. 

Mental  philosophy  (or  psycho- 
logy), definition  of,  i. 

Metaphor,  72. 

Method  as  applied  to  the  arrange- 
ment of  syllogisms  in  a  train 
of  reasoning,  156-159. 

Middle  term,  85. 

—  ambiguous,  87. 

—  sense  in  which  it  was  employ- 

ed by  Aristotle,  88. 

—  undistributed,  95,  142-143. 
Mnemonic  lines  for  the  syllogistic 

rules,  98. 

—  for  the  valid  moods,  103. 
Modality,  question  of,  26, 27, 1 28. 


Moods,  89. 

—  determination   of  the  legiti- 

mate, 90-92. 

—  indirect,  107-108. 

—  subaltern,  94,  104,  106-107. 

*  Most,*  '  many,*  &c.,  as  express- 
ing the  quantities  of  propo- 
sitions, 124-127,  129. 

• 

Nomen  infinitum  or  indefinitum, 

82. 

Odds,  meaning  of  the  expression, 

130. 
Oppositions,  77-80. 
•—  Aristotelian,  80. 

Paronymous    terms,    fallacy   of, 

153-154- 
Partition,  59. 

Perception,  definition  of,  i. 

Permutations,  82,  83. 

Predicables,    heads    of,    36-47, 

160-162. 

Predicate  of  a  proposition,  9,  23. 

—  its  relation  to  the  subject  of  a 

proposition,  39-47. 
Predicated,  meaning  of,  23,  24. 
Predication,  theory  of,  46,  47. 
Premisses,  10,  85. 

—  major  and  minor,  85. 

—  negative,  96. 

—  particular,  96-98. 
Principle  of  division,  59,  60. 
Probable,    signification    of   the 

word,  139,  132. 

—  reasoning,  128-139. 
Probability,  signification  of  the 

word,  130,  132. 


Probably,    signification    of  the 

word,  132. 
Problema,  85. 
Progressive  method,  157, 
Property,  40,  41. 

—  defined,  45. 

—  difficulty     of    distinguishing 

from  differentia,  55,  60. 

—  generic,  64-65. 

—  specific,  64-65. 
Propositions,  complex  (hypothe- 
tical), 1 1 2-1 14,  122-123. 

—  conjunctive    and  disjunctive, 

1 1 2-1 14. 

—  definition  of,  23. 

—  disjunctive,  dispute  as  to  their 

meaning,  118. 

—  division  of,  according  to  their 

quantity  and  quality,    28- 

32. 

—  employed    in    preference    to 

judgments,  7. 

—  import  of,  46,  47. 

—  instances  of,  9. 

—  quality  of,  as  expressed   by 

'most,'  *many,'  &c.,   124- 
127. 

—  secundi  adjacentis  and  tertii 

adjacentis,  11. 

—  verbal  and  real,  48. 

—  whose    copula    is    modified, 

128-129. 
Pro-syllogism,  109. 
Psychology,  definition  of,  i. 

—  its  relation  to  logic,  3. 

Qusestio,  86. 

Quality  of  propositions,  a 8. 


Quantification  of  the  subject,  29- 

30. 

—  predicate,  30-32. 

Quantity  of  propositions,  28-30. 

—  as  expressed  by  *  most,' '  many,* 

&c.,  124-127. 
Question — beggmg  epithets,  146. 

Real  propositions,  48. 
Reasoning,  probable,  128-139. 
Reduction,  100-104. 

—  ostensive,  1 00-101. 

—  per  impossibile,  100-104. 
Reflexion         (comparison        or 

thought),  definition  of,  i. 
Regressive  or  Goclenian  sorites, 
III. 

—  method,  157. 

^Tjnuov  of  Aristotle,  138. 
Separable  accident,  42,  43. 
Simple  ideas,  16. 
Singular  terms,  12. 

—  propositions  rank  as  univer- 

sal, 28,  29. 
Sorites,  109-1 11. 

—  Goclenian  or  regressive,  in. 
Special  rules  for  the  syllogistic 

figures,  105. 
Species,  38-39. 

—  cognate  or  co-ordinate,  64. 

—  co-ordinate  but  exclusive,  44. 

—  defined,  45. 

—  infima,  63-64,  66-67. 

—  overlapping,  43,  44. 

—  subaltern,  64. 
Subaltern  opposition,  78,  80. 

—  moods,  94,  104,  106-107. 


190 


INDEX. 


Subaltemation,  80. 
Sub-division,  63-64. 
Subject  of  a  proposition,  9,  23. 
Subordination,  80. 
Sufficient  reason,  law  of,  91. 
Syllogism,  ambiguity  of  the  word, 
8. 

—  is  the  a  petitio  principii,  146. 

—  legitimate  forms  of,  90-108. 

—  possible  forms  of,  88-90. 

—  structure  of  the,  84-88. 
2t/AXo7tff;x^s  fiovoK-fjfifMTOSj  86. 
Syllogisms,  complex    (hypothe- 
tical), 112-123. 

—  conjunctive,    114-116,    122- 

123. 

—  disjunctive,  116-118, 1 22-1 23. 
Syllogistic  rules,  95-100. 
Syncategorematic  words,  12. 
Synonyms,  37,  44. 
Synthetical  judgments,  48. 

Tautologous  propositions,  48. 
Terms,  connotation  and  denota- 
tion of,  19-22. 

—  contrary    and    contradictory, 

83. 


Terms,  definition  of,  11. 

—  employed    in    preference    to 

concepts,  7. 

—  distribution  of,  33-35. 

—  instances  of,  9. 

—  used  univocally,  equivocally, 

and  analogously,  86-87. 

—  various  kinds  of,  11-18. 
Thought,  definition  of,  1. 

—  or  thinking,  as  an  act  or  ope- 

ration, distinguished  from 
thought  or  thoughts,  as  a 
result,  2. 

—  its  relation  to  language,  7» 

—  its  products,  2. 
Trains  of  reasoning,  109. 

—  on  method  as  appliedj  to  the 

arrangement    of  syllogisms 

in,  156-159- 
Trilemma,  tetralemma,  &c.,  120. 

Undistributed  middle,  95,  142- 

143- 
Univocally,  terms  used,  86-87. 

Verbal  propositions,  48. 

—  fallacies,  87,  141. 


THE  END. 


BY  THE   SAME  AUTHOR. 


THE    ELEMENTS    OF    INDUCTIVE    LOGIC. 
Fourth  Edition,    ds. 


-M- 


BACON'S    NOVUM    OBaANUM. 
Edited  with  Introduction   and  Notes.     14J-. 


-M- 


LOOKE'S   CONDUCT   OF   THE   UNDERSTANDING. 
Edited  with.  Introduction  and  Notes.     ^ 

Second  Edition,    is. 


-¥¥• 


THE     PRINCIPLES      OF     MORALS. 

Introductory  Chapters. 

(Jointly  with  the  late  J.  M.  Wilson,  B.D.) 

8vo.  boards^  ^s.  6d. 


THE     PRINCIPLES     OF     MORALS. 

Part  II  (being  the  body  of  the  Work). 

By  Professor  Fowler,  D.D. 

8vo.  cloth  y  loj.  (id. 


-M- 


Oxford:  Clarendon  Press. 

London  :  Henry  Frowde,  Oxford  University  Press  Warehouse, 

Amen  Corner,  E.C. 


October,  1888. 

C!)e  Clatenoon  ipres:?,  S>]cfotD, 
LIST  OF  SCHOOL  BOOKS, 

PUBLISHED  FOR    THE   UNIVERSITY  BY 

HENBY    PBOWDE, 

AT  THE   OXFORD   UNIVERSITY  PRESS  WAREHOUSE, 
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•  • 


«*    AU  Books  art  hound  in  Cloihy  unless  otherwist  described* 


LATIN. 


Allen.  An  Elementary  Latin  Grammar,   By  J.  Barrow  Allen,  M.A. 

Fifty-seventh  Thousand Extra  fcap.  8vo.  2f.  td* 

Allen.    Rudimenta  Latina,    By  the  same  Author.    Extra  fcap.  8vo.  2 j. 

Allen.  A  First  Latin  Exercise  Book.  By  the  same  Author.  Fourth 
Edition Extra  fcap.  8vo.  2S.  6d, 

Allen.    A  Second  Latin  Exercise  Boott,    By  the  same  Author. 

Extra  fcap.  8vo.  31.  6<f . 
\A  Key  to  First  and  Second  Latin  Exercise  Books  :  for  Teachers  only.] 

Jerram.  Anglice  Reddenda;  or  Extracts^  Latin  and  Greek,  for 
Unseen  Translation,     By  C  S.  Jbrram,  M.A.     Fourth  Edition, 

Extra  fcap.  8vo.  u.  6</. 

Jerram.  Anglice  Reddenda,  Second  Series.   ByC.S.  Jerram, M.A. 

Extra  fcap.  8vo.  3^. 

Jerram.  Reddenda  Minora;  or.  Easy  Passages,  Latin  and  Greeks  for 
Unseen  Translation.  For  the  use  of  Lower  Forms.  Composed  and  selected 
by  C.  S.  Jerram,  M.A. Extra  fcap.  8vo.  xs,  6d, 

Lee-Warner.    Ifints  and  Helps  for  Laiin  Elegiacs, 

Ex{hi  fcap.  8vo.  3X.  6d, 
[A  Key  is  Provided:  for  Teachers  only.] 

Lewis  and  Short.  A  Latin  Dictionary^  founded  on  Andrews'  Edition 
of  Freund's  Latin  Dictionary.  By  Charlton  T.  Lewis,  Fh.D.,  and  Charles 
Short,  LL.D 4to.  25;. 

ZTunns.    First  Latin  Reader,   By  T.  J.  NuNNS,  M.A.     lliird  Edition, 

Extra  fcap.  8va  2X. 

FapUlon.  A  Manual  of  ComparaHve  Philology  as  applied  to  the  Illustra- 
tion of  Greek  and  Latin  Inflections.   By  T.  L.  Papillon,  M.A.    Third  Edition, 

Crown  Svo.  fa, 

Bamsay.  Exercises  in  Latin  Prose  Composition,  With  Introduction, 
Notes,  and  Passages  of  graduated  difficulty  for  Translation  into  Latin.  By 
G.  G.  Ramsay,  M.A.,  Professor  of  Humanity,  Glasgow.     SecoTtd  Edition. 

Extra  fcap.  Svo.  4J.  td, 

Barsrent.  Easy  Passages  for  Translation  into  Latin,  By  J.  Y.  Sargent, 

M.A.    Seventh  Edition. Extra  fcap.  Svo.  as,  6d, 

[A  Key  to  this  Edition  is  provided:  for  Teachers  only.] 
Sarg^ent.     A  Latin  Prose  Primer.     .        .         Extra  fcap.  Svo.  2s.  6d. 

s  

[1 


II 


Caesar.  The  Commentaries  (for  Schools).  With  Notes  and  Maps. 
By  Charles  E.  Moberly,  M.A. 

The  Gallic  War,    Second  Edition    ,         .        ,        ,     Extra  fcap.  8vo.  4*.  6d, 

The  Gallic  IFar.     Books  1,  II Extra  fcap,  8vo.  2S. 

The  Civil  War Extra  fcap.  8vo.  3^.  td. 

The  Civil  War.    Book  I.    Second  Edition.     .        .  Extra  fcap.  8vo.  2*. 

Catnlli   Veronensls     Carmina    Selecta^    secundnm     recognitionem 
Robinson  Ellis,  A.  M.    .       .  ....     Extra  fcap.  8vo.  3J.  6</. 

Cloero.     Selection  of  interesting  and  descriptive  passages.    With  Notes. 
By  Henry  Walford,  M.A.    In  three  Parts.     Third  Edition. 

Extra  fcap.  8vo.  4; .  (>d. 
Part  I.      Anecdotes  front  Grecian  and  Roman  History.        .        limp,  \s.  6d. 
Part  II.     Omens  and  Dreams ;  Beauties  of  Nature.     .        .        limp,js.6d, 
Vaxl  III.  Rome's  Rule  of  her  Provinces.         ....        limp,u.(>d. 

Cicero.    De  Senectute.    With  Introduction  and  Notes.    By  Leonard 
Huxley,  B.  A.    In  one  or  two  Parts     ....        Extra  fcap.  8vo.  2 j. 

Cicero.  Pro  Cluentio.   With  Introduction  and  Notes.   By  W.  Ramsay, 
M.A.    Edited  by  G.G.Ramsay,  M.A.   Second  Edition.   Extra  fcap.  Svo.  3J.  6</. 
Cloero.    Selected  Letters  (for  Schools).     With   Notes.    By  the  late 
C.  E.  Prichard,  M JL,  and  E.  R.  Bernard,  MA.    Second  Edition. 

Extra  fcap.  8vo.  31. 
Cicero.     Select  Orations  (for  Schools).    First  Action  against  Verres  ; 

Oration  concerning  the  command  oj  Gnaeus  Pomfieius  ;  Oration  on  behalf  of 

Archias;  Ninth  Philippic  Oration.    With  Introduction  and  Notes.     By  J.  R. 

King,  M.A.    Second  Edition.  ....         Extra  fcap.  8vo.  us.  6d. 

Cicero.     In  Q.  Caecilium  Divinatio  and  In  C.  Verrem  Actio  Prima. 

With  Introduction  and  Notes.    By  J.  R.  King,  M.A. 

Extra  fcap.  8vo.  limp,  is.  6d. 
Cicero.    Speeches  against  Catilina.    With  Introduction  and  Notes.    By 

E.  A.  Upcott,  M.A.    In  one  or  two  Parts.        .        .        Extra  fcap.  8vo.  2s.  6d. 

Cicero.  Philippic  Orations.  With  Notes,  &c.  by  J.  R.  King,  M.A. 
Second  Edition 8vo.  lar.  6d, 

Cicero.  Select  Letters.  With  English  Introductions,  Notes,  and  Ap- 
pendices.   By  Albert  Watson,  M.A.     Third  Edition.      .      .      .      8vo.  iSj. 

Cicero.     Select  Letters,    Text.    By  the  same  Editor.     Second  Edition. 

Extra  fcap.  8va  4*. 

Comelins    Nepos.     With   Notes.      Bv   OscAR   Browning,   M.A. 

Third  Edition.     Revised  by  W.  R.  Inge,  M.A.    .         .         Extra  fcap.  8vo.  3*. 

Horace.  With  a  Commentary.  Volume  I.  The  Odes,  Carmen 
Seciilare,  and  Epodes.  By  Edward  C.  Wickham,  M.A.,  Head  Master  of 
Welhngton  College.    New  Edition.    In  one  or  two  Parts.     Extra  fcap.  8vo.  6s. 

norace.  Selected  Odes.  With  Notes  for  the  use  of  a  Fifth  Form.  By 
E.  C.  Wickham,  M.A.     In  one  or  two  Paris.        .        .        Extra  fcap.  8vo.  2j. 

Juvenal.  XIII  Satires.  Edited,  with  Introduction,  Notes,  etc.,  by 
C.  H.  Pearson,  MA.,  and  H.  A.  Strong,  M.A.    .       .        .        Crown  8vo.  6j. 

Or  separately,  Text  and  Introduction,  35,;  Notes,  35.  6d. 

tlvy.     Selections  (for  Schools).    With  Notes  and  Maps.     By  H.  Lkk- 

Warner,  M.A Extra  fcap.  8vo 

Part  I.       The  Caudine  Disaster,       .        ,        .        ,        ,  limp,  is.  6d. 

Part  II.    HannibaTs  Campaign  in  Italy.          ....      limp,  ij.  td. 
Part  III.  The  Macedonian  War, Ump,  i* .  td. 


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Xdvy.  Book  I.  With  Introduction,  Historical  Examination,  and  Notes. 
By  J.  R.  Seeley  M.A,    Second  Edition,  .....        8vo.  6j. 

Uvy.  Books  V—  VII.  With  Introduction  and  Notes.  By  A.  R.  Cluer, 
B.A.  Second  Edition.  Revised  by  P.  E.  Matheson,  M.A.  In  one  or  two 
parts, Extra  fcap.  8vo.  5; . 

Idvy.  Books  XXI^XXIII,  With  Introduction  and  Notes.  By 
M.  T.  Tatham,  M.A. Extra  fcap.  8vo.  \s.  td, 

Iiivy.  Book  XXII.  With  Introduction  and  Notes.  By  the  same 
Editor Extra  fcap.  Bvo.  2.s.  td. 

Ovid.  Selections  (for  the  use  of  Schools).  With  Introductions  and 
Notes,  and  an  Appendix  on  the  Roman  Calendar.  By  W.  Ramsay,  MA. 
Edited  by  G.  G.  Ramsay,  M.A.    Third  Edition.      .      Extra  fcap.  8vo.  5*.  td, 

Ovid.    THstia,  Book  I.    Edited  by  S.  G.  Owen,  B.A. 

Extra  fcap.  8vo.  3;.  td. 

Per  sins.  The  Satires.  With  Translation  and  Comncentary  by 
J.  Conington,  M.A.,  edited  by  H.  Nettleship,  M.A.    Second  Edition. 

8vo.  75.  td. 

Flantus.  Captivi.  With  Introduction  and  Notes.  By  W.  M.  Lindsay, 
M.A.    In  one  or  two  Parts.        \        ,        ,        .        .        Extra  fcap.  8vo.  2s.  td, 

Plantus.  Trinummus.  With  Notes  and  Introductions.  By  C.  E. 
Freeman,  M.A.  and  A.  Sloman,  M.A.     ....        Extra  fcap.  8vo.  3^ . 

Fllny.  Selected  Letters  (for  Schools).  With  Notes.  By  the  late 
C.  E.  Prichard,  M.A.,  and  E.  R.  Bernard,  M.A.  New  Edition.  In  one  or 
two  Parts. Extra  fcap.  8vo.  3* . 

Sallnst.  Bellum  Catilinarium  and  Jugurthinum.  With  Introduc- 
tion and  Notes,  by  W.  W.  Capes,  M.A.      .        .        .       Extra  fcap.  8vo.  4^.  td. 

Tacitns.  The  Annals.  Books  I — IV.  Edited,  with  Introduction  and 
Notes  for  the  use  of  Schools  and  Junior  Students,  by  H.  Furneaux,  M.A. 

Extra  fcap.  8vo.  5^. 

Tacitns.     The  Annals,    Book  I.     By  the  same  Editor. 

Extra  fcap.  Bvo.  livip,  2s, 

Terence.  Adelphi.  With  Notes  and  Introductions.  By  A.  Sloman, 
M.A- ."*      Extra  fcap.  8vo.  3J. 

Terence.  Andria,  With  Notes  and  Introductions.  By  C.E.  Freeman, 
M.A.,  and  A.  Sloman,  M.A. Extra  fcap.  8vo.  3^. 

Terence.  Phormio.  With  Notes  and  Introductions.  By  A.  Sloman, 
M.A Extra  fcap.  8vo.  3^. 

Tibnllns  and  Fropertins.  Edited,  with  Introduction  and  Notes,  by 
G.  G.  Ramsay,  M.A.    In  one  or  two  Parts.    ,        ,       ,       Extra  fcap.  8vo.  6^. 

Virsril.  With  Introduction  and  Notes,  by  T.  L.  Papillon,  M.A. 
In  Two  Volumes.    .        .        .         Crown  8vo.  loj .  td.  \  Text  separately,  4J.  td, 

Virgril.  Bucolics.  With  Introduction  and  Notes,  by  C.  S.  Jerram,  M.A. 

In  «ne  or  two  Parts.    Extra  fcap.  8vo.  is.  td. 

Vlrfifil.  Aeneidl.  With  Introduction  and  Notes,  by  C.  S.  Jerram,  M.A. 

Extra  fcap.  8vo.  ///;//,  xs.  td, 

Virgil.  Aeneid  IX,  Edited  with  Introduction  and  Notes,  by  A.  E. 
Haigh,  M.A.         ,        ,        .        Extra  fcap  8vo. //V«/ iJ.  6</.    In  two  Parts,  is. 


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GREEK. 

Chandler.  Tht  Elements  of  Greek  Accentuation  (for  Schools). 
By  H.  W.  Chandler,  M.A.     Second  Edition.         ,        Extra  fcap.  8vo.  2j.  6^. 

Zilddell  and  Scott.  A  Greek-English  Lexicon^  by  Henry  George 
LiDDELL,  D.D.,  and  Robert  Scott,  D.D.    Seventh  Edition.        ,        410.  36^. 

Llddell  and  Scott.  A  Greek-English  Lexicon,  abridged  from  Liddell 
and  Scott's  4to.  edition,  chiefly  for  the  use  of  Schools.      T7venty-first  Edition, 

Square  izmo.  7*.  6d. 

Voitcli.  Greek  Verhs^  Lrregular  and  Defective :  their  forms,  meaning, 
and  quantity  ;  embracing  all  the  Tenses  used  by  Greek  writers,  with  references 
to  the  passages  in  which  they  are  found.  By  W.  Veitch,  LL.D.  Fourth  Edition. 

Crown  8vo.  \os.  6d. 

Wordsworth,  Graecae  Grammaticae  Rudimenta  in  usum  Scholarum. 
Auctore  Carolo  Wordsworth,  D.CL.    Nineteenth  Edition.       .       i2mo.  4^. 

Wordsworth.  A  Greek  Primer^  for  the  use  of  beginners  in  that 
Language.  By  the  Right  Rev,  Charles  Wordsworth,  D.CL.,  Bishop  of 
St.  Andrew's.    Seventh  Edition.        ....         Extra  fcap.  8vo.  u.  td. 

Wright.  TTie  Golden  Treasury  of  Ancient  Greek  Poetry ;  being  a 
Collection  of  the  finest  passages  in  the  Greek  Classic  Poets,  with  Introductory 
Notices  and  Notes.     By  R.  S.  Wright,  M.A. .      .      New  edition  in  the  Press. 

Wrigrht  and  Shadwell.  A  Golden  Treasury  of  Greek  Prose  ;  being 
a  Collection  of  the  finest  passages  in  the  principal  Greek  Prose  Writers,  with 
Introductory  Notices  and  Notes.  By  R.  S.  Wright,  M.A.,  and  J.  E.  L.  Shad- 
WELL,  M.A. Extra  fcap.  Svo.  4^.  6</. 


A  SERLES  OF  GRADUATED  READERS.^ 

Easy  Greek  Reader,    By  Evelyn  Abbott,  M.A.    In  one  or  two 
Parts Extra  fcap.  Svo.  3X. 

First  Greek  Reader.  By  \V.  G.  Rushbrooke,  M.L.,  Second 
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Second  Greek  Reader,     By  A.  M.  Bell,  M.A. 

Extra  fcap.  Svo.  3J.  (>d. 

Fourth  Greek  Reader  ;  being  Specimens  of  Greek  Dialects.  With 
Introductions  and  Notes.  By  W.  W.  Merry,  D.D.,  Rector  of  Lincoln 
College Extra  fcap.  Svo.  4^.  dd. 

Fifth  Greek  Reader.  Selections  from  Greek  Epic  and  Dramatic 
Poetry,  with  Introductions  and  Notes.     By  Evelyn  Abbott,  M.A. 

Extra  fcap.  Svo.  4 J.  6d. 

THE  GREEK  TESTAMENT,-^ 

Evangfelia  Sacra  Oraece.        .        .        .        Fcap.  Svo.  limp^  is.  6d. 

The  Greek  Testament,  with  the  Readings  adopted  by  the  Revisers  of 
the  Authorised  Version. 

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XTovTun  Testamentnm  Graece  juxta  Exemplar  Millianum. 

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Zrovnm  Testamentnm  Graece.  Accedunt  parallela  S.  Scripturac 
loca,  necnon  vetus  capitulorum  notatio  et  canones  Eusebii.  Edidit  Carolus 
Lloyd,  S.T.P.R.,  necnon  Episcopus  Oxoniensis. 

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A  Greek  Testament  Primer.  An  Easy  Grammar  and  Reading 
Book  for  the  use  of  Students  beginning  Greek.    By  Rev.  E.  Miller,  M.A. 

Extra  fcap.  Svo.  3* .  6J. 

Outlines  of  Textual  Criticism  applied  to  the  New  Testament. 
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Aeschylns.  Agamemnon.    With  Introduction  and  Notes,  by  Arthur 

SiDGVViCK,  M.A.     Third  Editiofi.    In  one  or  two  Parts    .    Extra  fcap.  Svo.  3s. 

Aeschylns.     Choephoroi.    With  Introduction  and  Notes,  by  the  same 

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Aristophanes.    The  Clouds.  With  Introduction  and  Notes,  by  W.  W. 

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Cebes.    Tabula,    With  Introduction  and  Notes,  by  C.  S.  Jerram,  M.A. 

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Demosthenes.  Orations  against  Philip.  With  Introduction  and  Notes. 
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Euripides.    Alcestis.    By  C.  S.  Jerram,  M.A.    Extra  fcap.  Svo.  2J.  dd. 
Euripides.     Hecnba.    By  C.  II.  Russell.    Immciiiately. 
Euripides.    Helena.     By  the  same  Editor.      .     ^  Extra  fcap.  Svo.  zs. 
Euripides.     Heracleidae.     By  the  same  Editor.     Extra  fcap.  Svo.  3^. 
Euripides.  IphigeniainTauris,  With  Introduction  and  Notes.  By  the 

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Euripides.     Medea.    With  Introduction,  Notes  and  Appendices.    By 

C.  B.  Heberden,  M.A.    In  one  or  two  Parts.        .        .        Extra  fcap.  Svo.  2,t. 
Herodotus.     Book  IX.     Edited  with  Notes,  by  Evelyn  Abbott, 

M.A.    In  one  or  two  Parts Extra  fcap.  Svo.  3 j. 

Herodotus.  Selections.  Edited,  with  Introduction,  Notes,  and  a  Map, 
by  W.  W.  Merry,  D.D. Extra  fcap.  Svo.  2^.  td. 

Homer.  Iliad^  Books  I -XII.  With  an  Introduction,  a  brief 
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Homer.     Iliad^  Book  I.    By  the  same  Editor.     Third  Edition. 

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Bomer.     Odyssey ^  Books  XIII-XXIV.    By  the  same  Editor.     Second 
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Lncian.     Vera  Historia,    By  C.  S.  Jerram,  M.A.      Second  Edition, 

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Plato.    TJie  Apology.    With  Introduction  and  Notes.    By  St.  George 

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Plato.  Meno.  With  Introduction  and  Notes.  By  St.  George  Stock, 
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Sophocles.  (For  the  use  of  Schools.)  Edited  with  Introductions  and 
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Theocritus.  Edited,  with  Notes,  by  H.  Kynaston,  D.D.  (late 
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Zenophon.     Easy  Selections  (for  Junior  Classes).    With  a  Vocabulary, 

Notes,   and   Map.     By  J.  S.  Phillpotts,  B.C.L.,  Head  Master  of  Bedford 
School,  and  C.  S.  Jerram,  M.A.     Third  Edition,      ,     Extra  fcap.  Svo.  3^.  td. 

Zenophon.  Selections  (for  Schools).  With  Notes  and  Maps.  By 
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Zenophon.  Anabasis,  Book  I.  With  Notes  and  Map.  By  J.  Marshall, 
M.A.,  Rector  of  the  High  School,  Edinburgh.   .       .        Extra  fcap.  Svo.  2J.  dd. 

Zenophon.  Anabctsis,  Book  II.  With  Notes  and  Map.  By  C.  S. 
Jerram,  M.A Extra  fcap.  Svo.  2s. 

Zenophon.    Anabasis,  Book  III.    By  J.  Marshall,  M.A. 

Extra  fcap.  Svo.  2*.  6d. 
Zenophon.     Vocabulary  to  the  Anabasis.    By  J.  Marshall,  M.A. 

Extra  fcap.  Svo.  is.  6d. 

Zenophon.  Cyropaedia,  Book  I.  With  Introduction  and  Notes.  By 
C   Bigg,  D.D.  ..,,..,.        Extra  fcap.  Svo.  is. 

Zenophon.  Cyropaedia,  Books  IV,  V.  With  Introduction  and  Notes, 
by  C.  Bigg,  D.D Extra  fcap.  Svo.  is.  6d. 

Zenophon.  Hellenica,  Books  I,  II.  With  Introduction  and  Notes. 
By  G.  E.  Underhill,  M.A v        •        Extra  fcap.  Svo.  3s. 


LIST  OF  SCHOOL  BOOKS. 


EARLY  AND  MIDDLE  ENGLISH,  &c. 

Mayhew  and  Skeat.  A  Concise  Dictionary  of  Middle  English.  By 
A.  L.  Mavhew,  M.A.,  and  \V.  W.  Skeat,  Litt.  D.    .        .        Crown  Svo.  7^.  6d. 

Skeat.  A  Concise  Etymological  Dictionary  of  the  English  Language, 
By  W.  W.  Skeat,  Litt.  D.    Third  Edition.      .       •        ,       Crown  Svo.  s^.  (td. 

Tancock.  An  Elementary  English  Grammar  and  Exercise  Book. 
By  O.  W.  Tancock,  M.A.,  Head  Master  of  King  Edward  VI's  School,  Norwich. 
Second  Edition.  .......        Extra  fcap.  Svo.  is.  6d, 

Tancock.  An  English  Grammar  and  Reading  Book,  for  Lower 
Forms  in  Classical  Schools.    By  O.  W.  Tancock,  M.A.    Fourth  Edition. 

Extra  fcap.  Svo.  3*.  6d. 

Skeat.  The  Principles  of  English  Etymology.  First  Series.  By 
W.  W.  Skeat,  Litt.  D Crown  Svo.  9^. 

Earle.     The  Philology  of  the  English  Tongue,    By  J.  Earle,  M.A., 

Professor  of  Anglo-Saxon.    Fourth  Edition.      ,       ,      Extra  fcap.  Svo.  7^.  6t/. 

Earle.    A  Book  for  the  Beginner  in  Anglo-Saxon,  By  the  same  Author. 

-  Third  Edition Extra  fcap.  Svo.  is.  6d. 

Sweet.  An  Anglo-Saxon  Primer,  with  Grammar,  Notes,  and  Glossary, 
By  Henry  Sweet,  M.A.     Third  Edition.        .        .       Extra  fcap.  Svo.  is.  6d. 

Sweet.  An  Anglo-Saxon  Reader.  In  Prose  and  Verse.  With  Gram- 
matical Introduction,  Notes,  and  Glossary.  By  the  same  Author.  Fourth 
Edition,  Revised  and  Enlarged Extra  fcap.  Svo.  Zs.  6d. 

Sweet.     A  Second  Anglo-Saxon  Reader.     By  the  same  Author. 

Extra  fcap.  Svo.  45.  td. 

Sweet.    Anglo-Saxon  Reading  Primers. 

I.    Selected  Homilies  of  Mlfric.  Extra  fcap.  Svo.  siij^  covers,  is.  6d. 

IL    Extracts  front  Alfreds  Orosius.  Extra  fcap.  Svo.  stiff  covers,  is.  6d, 

Sweet.  First  Middle  English  Primer ,  with  Grammar  and  Glossary, 
By  the  same  Author Extra  fcap.  Svo.  is. 

Sweet.  Second  Middle  English  Primer.  Extracts  from  Chaucer,  with 
Grammar  and  Glossary.    By  the  same  Author.        .        .        Extra  fcap.  Svo.  is. 

Morris  and  Skeat.  Specimens  of  Early  English.  A  New  and  Re- 
vised Edition.   With  Introduction,  Notes,  and  Glossarial  Index. 

Part  I.  From  Old  English  Homilies  to  King  Horn  (a.d.  1150  to  a.d.  1300). 

By  R-  Morris,  LL.D.     Second  Edition        .        .        Extra  fcap.  Svo.  oj. 
Part  IL  From  Robert  of  Gloucester  to  Gower  fA.D.  1208  to  a.d.  1393).    By  R. 

Morris,  LL.D.,  and  W.  W.  Skeat,  Litt.  D.     Third  Edition 

Extra  fcap.  Svo.  7^ .  (>d, 

Skeat.  Specimens  of  English  Literature,  from  the  'Plouj^hmans 
Crede'  to  the  *  Shepheardes  Calender'  (a.d  1394  to  A. p.  1579).  With  Intro^ 
duction,  Notes,  and  Glossarial  Index.  By  W.  W.  Skeat,  Litt.  D.  Fourth  Edition. 

Extra  fcap.  Svo.  7*.  td. 

Typical  Selections  from  tlie  best  Engrlisli  Writers,  with  Intro- 
ductory Notices.  Second  Edition.  In  Two  Volumes.  Vol.  I.  Latimer  to 
Berkeley.     Vol.  II.  Pope  to  Macaulay.      .      .      Extra  fcap.  Svo.  3^.  dd.  each. 


8 


CLARENDON  PRESS 


A  SERIES  OF  ENGLISH  CLASSICS, 

Lan^land.     TTie  Vision  of  William  concerning  Piers  the  Plowmant 

by  WiLLiAAi  Langland.    Edited  by  W,  W.  Skkat,  Litt.  D.   Fourth  Edition. 

Extra  fcap.  8vo.  4^.  (>d. 

Chancer.  I.  The  Prologue  to  the  Canterbury  Tales ;  The  Knightes 
Tale;  The  Nonne  Prestes  Tale.  Edited  by  R.Morris,  LL.D.  Fifty-first 
T/umsand. Extra  fcap.  8vo.  zs.  6d. 

Chancer.  II.  The  Prioresses  Tale  ;  Sir  Thopas  ;  The  Monkes  7 ale  ; 
TheClerkes  Tale;  The  Squures  Tale,  ^c.  Edited  byW.W.  Skeat,  Litt.  D. 
Third  Edition Extra  fcap.  8vo.  45.  6d. 

Chancer.    III.  The  Tale  of  the  Man  of  Lawe  ;  The  Pardoneres  Tale  ; 

The  Secofid  Nonnes    Tale;    Tht  Chanouns  Yetnannes    Tale.     By  the  same 
Editor.     New  Edition,  Revised Extra  fcap.  Svo.  4J.  (id. 

Oamelyn,  The  Tale  of.    Edited  by  W.  W.  Skeat,  Litt.  D. 

Extra  fcap.  Svo.  stiff  covers,  15.  ftd. 

Minot.  The  Poems  of  Laurence  Minot,  Edited,  with  Introduction 
and  Notes,  by  Joseph  Hall,  M.A.  .        .        .        Extra  fcap.  Svo.  45.  6d. 

Wycllffe.  The  New  Testament  in  English,  according  to  the  Version 
by  John  Wycliffk,  about  a.d.  1380,  and  Revised  by  John  Purvey,  about 
A.D.  1388.    With  Introduction  and  Glossary  by  W.  W.  Skkat,  Litt.  D. 

Extra  fcap.  Svo.  ts. 

Wycllffe.     The  Books  of  Job,  Psalms,  Proverbs,  Ecclesiastes,  and  the 

So7ig  cf  Solomon',  according  to  the  Wycliffite  Version  made  by  Nicholas  db 
Hereford,  about  a.d.  1381,  and  Revised  by  John  Purvey,  about  a.d.  1388. 
With  Introduction  and  Glossary  by W.W.  Skeat,  Litt.  D.  Extra  fcap.  Svo.  3^.  td. 

Spenser.     The  Faery  Qucene.    Books  I  and  II.    Edited  by  G.  W. 

KlTCHlN,  D.D. 

Book  I.     Tenth  Edition.                ....         Extra  fcap.  Svo.  is.  hd. 
Book  II.  Sixth  Edition Extra  fcap.  Svo.  zs,  6d. 

Hooker.  Ecclesiastical  Polity,  Book  I.  Edited  by  R.  W.  Church, 
M.  A.,  Dean  of  St.  Paul's.    Second  Edition.       .        .        .     Extra  fcap.  Svo.  2j, 

Marlowe  and  Greene. — Marlowe's  Tragical  History  of  Dr.  Faustus^ 

and    Greene's    Honourable   History  of  Friar  Bacon    and  Friar  Bungay. 
Edited  by  A.  W.  Ward,  M.A.    New  Edition.    .        .        Extra  fcap.  Svo.  6.?.  td. 

Marlowe.  Edward  II,  Edited  by  O.  W.  Tancock,  M.A.  Second 
Edition Extra  fcap.  8va  Paper  covers,  zs.    cloth,  3J. 

Shakespeare.    Select  Plays.    Edited  by  W.  G.  Clark,  M.A.,  and 

W.  Alois  Wright,  M.A. Extra  fcap.  Svo.  stiff  covers. 

The  Merchant  of  Venice,    is.  Macbeth,     is.  6d, 

Richard  the  Second,    is.  6d.  Hanilet,    as. 

Edited  by  W.  Aldis  Wright,  M.A. 

The  Tempest,     is.  6d.  CorioUmus.     7S.  Sd. 

As  You  Like  It.     is.  td.  Richard  the  Third,    aj.  6ci 

A  Midsummer  Night's  Dream,  is,  6dt  Henry  the  Fijth.    2j. 

Twelfth  Night,    is.td.  King  John.    is.6d. 

Julius  Caesar.    2s.  King  Lear,    is.  td. 


LIST  OF  SCHOOL  BOOKS, 


Shakespeare  as  a  Dramatic  Artist ;  a  popular  Illustration  of  tht 
Principles  cj  Scientific  Criticism.     By  R.  G.  Moulton,  M.A.    Crowrn  Svo.  5J. 

Bacon.    Advancement  of  Learning,  Edited  by  W.  Aldis  Wright, 

M.A,     Third  Edition Extra  fcap.  Svo.  4^.  6</. 

Milton.    I.  Areopagitica.     With  Introduction  and  Notes.    By  John 
W.  Hales,  M.A.      Third  Edition Extra  fcap.  Svo.  3*. 

Milton.    II.  Poems.    Edited  by  R.  C.  Browne,  M.A.    a  vols.   Fifth 
Edition.         .    Extra  fcap.  Svo.  6s.  td.    Sold  separately,  Vol.  I.  \s..  Vol.  II.  3*. 

In  paper  covers  : — 
Lycidas,  id.        V Allegro,  yl.        II Penseroso,  ^d.        Comus^td. 

Milton.     III.  Paradise  Lost.     Book  I.     Edited  with  Notes,  by  H.  C. 
Beeching,  M.A.       .        Extra  fcap.  Svo.  is.  td.     hi  white  Parchment,  35.  td. 

Milton.    IV.  Samson  Agonistes.    Edited  with  Introduction  and  Notes 
by  John  Churton  Collins.        .        .        .        Extra  fcap.  Svo.  stiff  covers,  is. 

Clarendon.      History  of  the   Rebellion.     Book   VI.        Edited  with 
Introduction  and  Notes  by  T.  Arnold,  M.A.     .        .     Extra  fcap.  8va  4^.  td. 

Bunyan.       The  Pilgrim^ s  Progress,    Grace  Abounding^  Relation   cf 
the  Imprisonment  of  Mr.  John  Bunyan.    Edited  by  E.  Vknabi.es,  M.A. 

Extra  fcap.  Svo.  54".     In  white  Parchment,  ts. 

Dryden.     Stanzas  on  the  Death  of  Oliver  Cromwell ;  Astnra  Redux  ; 

Annus  Mirabilis  ;  Absalom  and  Achitophel;  Religio  Laid:  The  Hind  and 
tlie  Panther.    Edited  by  W.  D.  Christie,  M.A.       .      Extra  fcap.  Svo.  3*.  td. 

Locke's  Conduct  of  the  Understanding.     Edited,  with  Introduction, 
Notes,  &c.  by  T.  Fowler,  D.D.    Second  Editiott.     .     .     Extra  fcap.  Svo.  2*. 

Adflison.     Selections  from  Papers  in  the   *  Spectator.*    With  Notes. 
By  T.  Arnold,  M.A.    .        Extra  fcap.  Svo.  4^.  td.    In  white  Parchment,  ts. 

Steele.     Selected  Essays  from  the  Tatler,  Spectator,  and  Guardian.   By 
Austin  Dobson,        .        .     Extra  fcap.  Svo.  5J.    In  white  Parchment,  ts.  td. 

Berkeley.     Select  Works  of  Bishop  Berkeley,  with  an  Introduction  and 
Notes,  by  A.  C.  Eraser,  LL.D.     Third  Edition.        ,        .    Crown  Svo.  7.1.  td. 

Pope.    I.  Essay  on  Man,    Edited  by  Mark  Pattison,  B.D.    Sixth 
Edition, Extra  fcap.  Svo.  is.  td. 

Pope.  II.  Satires  and  Epistles,    By  the  same  Editor.   Second  Edition, 

Extra  fcap.  Svo.  iS, 

Parnell.     7 he  Hermit, Paper  covers,  2d. 

Johnson.     I.     Rasselas.     Edited,  with  Introduction   and   Notes,  by 
G.  Birkbeck  Hill,  D  .C.L.    Extra  fcap.Svo.  lijftp,  2s.  In  white  Parchment, ^s.td. 

Johnson.     II.  Rasselas ;   Lives  of  Dryden  and  Pope.      Edited   by 
Alfred  Milnes,  M.A Extra  fcap.  Svo.  \s.  td. 

Lives  of  Pope  and  Dryden Stiff  covers,  is.dd, 

Johnson.     III.  Life  of  Milton.     Edited,  with  Notes,  etc.,  by  C.  H. 
Firth,  M.A.       .        .        .        lLxixa.{cdi^.^vo.sti^ covers,  is  td.\  cloth,  2s.  td. 

Johnson.     IV.    Vanity  of  Human   Wishes,    With  Notes,  by  E.  J. 
PayNk,  M.A. Paper  covers,  ^d. 


10 


CLARENDON  PRESS 


Gray.    Selected  Poems.     Edited  by  Edmund  Gosse. 

Extra  fcap.  8vo.    Stiff  covers^  is.  6d,    In  white  Parchment^  3*. 
O-ray.    Elegy,  and  Ode  on  Eton  College.      .        .        Paper  covers,  2d, 

Goldsmith.    Selected  Poems.    Edited,  with  Introduction  and  Notes,  by 

Austin  Dobson Extra  fcap.  8vo.  35.  6d, 

In  white  Parchment,  4^.  6d, 

Goldsmith.     Tke  Traveller.    Edited  by  G.  Birkijeck  Hill,  D.C.L. 

Extra  fcap.  8vo.  stiff  covers,  is. 
The  Deserted  Village Paper  covers,  2d. 

Cowper.    I.  The  Didactic  Poems  tf/  1782,  with  Selections  from  the 
Minor  Pieces,  a.d.  1779-1783.    Edited  by  H.  T.  Griffith,  B.A. 

Extra  fcap.  8vo.  3*. 
Cowper.     II.  The   Task,  with  Tirocinium,  and  Selections  from  the 
Minor  Poems,  a.d.  1784-1799.     By  the  same  Editor.    Second  Edition. 

M      Extra  fcap.  8vo.  3*. 

Burke.    I.    Thoughts  on  the  Present  Discontents;  the  two  Speeches 
on  America.    Edited  by  E.  J.  Paynh,  M.  A.    Second  Edition. 

Extra  fcap.  8vo.  ^.  6d. 

Bnrke.     II.    Reflections  on   the  French  Revolution.     By  the  same 
Editor.    Second  Edition Extra  fcap.  8vo.  5*. 

Burke.     III.    Four  Letters    on    the   Proposals  for  Peace  with    the 
Regicide  Directory  of  France.     By  the  same  Editor.    Second  Edition. 

Extra  fcap.  8vo.  5^. 

Hyperion,  Book  I.    With  Notes,  by  W.  T.  Arnold,  B.A. 

Paper  covers^  4<f. 

Childe  Harold.  With  Introduction  and  Notes,  by  H.  F.  Tozer, 

Extra  fcap.  8vo.  31.  dd.    In  white  Parchment,  55. 

Lay  of  the  L^ast  Minstrel.     Edited  with  Preface  and  Notes  by 
W.  MiNTo,  M.A.     With  Map. 

Extra  fcap.  8vo.  stiff  covers,  2S.     In  Ornamental  Parchment,  y.  dd. 

Scitt.    Lay  of  the  Last  Minstrel.    Introduction  and  Canto  I,   with 
Preface  and  Notes  by  W.  M INTO,  M.  A Paper  covers,  (id. 


Seats. 

Byron. 
M.A. 

Scott. 


PBENCH  AIS^D  ITALIAN. 

Brachet.     Etymological  Dictionary  of  the  French  Language,   with 

a  Preface  on  the  Principles  of  French  Etymology.    Translated  into  English  by 
G.  W.  KiTCHiN,  D.D.,  Dean  of  Winchester.     Third  Edition. 

Crown  8vo.  js.  6d. 

Brachot.    Historical  Grammar  of  the  French  Language.    Translated 
into  English  by  G.  W.  Kitchin,  D.D.    Fourth  Edition. 

Extra  fcap.  8vo.  3^.  td. 

SaintsTjnry.    Primer  of  French  Literature,     By  George  Saints- 
bury,  M.A.    Second  Edition. Extra  fcap.  8vo.  2*. 

Saintsbnry.     Short  History  of  French  Literature.     By  the  same 
Author. Crown  8vo.  \os.  td. 

Saintsbnry.    Specimens  of  French  Literature.      .        .    Crown  8vo.  9*. 


I 


LIST  OF  SCHOOL  BOOKS. 


II 


Beanmarcbais.  Le  Barbier  de  Shfille.  With  Introduction  and  Notes 
by  Austin  Dobson. Extra  fcap.  8vo.  2s.  6d. 

Blonet.  L'Aloquence  de  la  Chaire  et  de  la  .  Tribune  Fran^aises. 
Edited  by  Paul  Blouet,  B.A.  (Univ.  Gallic.)  Vol.  I.  French  Sacred  Oratory. 

Extra  fcap.  8vo.  25. 6d. 

Corneille.  Horace.  With  Introduction  and  Notes  by  George 
Saintsbury,  M.A. Extra  fcap.  8vo.  2s.  dd. 

CorneiUe.  Cinna.  With  Notes,  Glossary,  etc.  By  Gustave  Masson, 
B.A Extra  fcap.  8vo.  stiff  covers,  is.dd.   cloth,  2s. 

Oantier  (Theophile).  Scenes  of  Travel.  Selected  and  Edited  by 
G.  Saintsbury,  M  JL Extra  fcap.  8vo.  is. 

Masson.  Louis  XIV  and  his  Contemporaries ;  as  described  in  Ex- 
tracts from  the  best  Memoirs  of  the  Seventeenth  Century.  With  English  Notes, 
Genealogical  Tables,  &c.    By  Gustavk  Masson,  B.A.      Extra  fcap.  8vo.  2s.  td. 

Molidre.  Les  PrScieuses  Ridicules.  With  Introduction  and  Notes  by 
Andrew  Lang,  M.A Extra  fcap.  8vo.  is.  td. 

Molidre.  Les  Femmes  Savantes.  With  Notes,  Glossary,  etc.  By 
Gustave  Masson,  B.A.       ,        Extra  fcap.  8vo.  stiff  covers,  is.  6d.    cloth,  as, 

Molidre.     Les  Fourberies  de  Scapin.  \  With  Voltaire's  Life  of  Moliere.      By 
^      .  A^i.    T  \      Gustave  Masson,  B.A. 

Bacine.     Atnalie.  \  Extra  fcap.  8vo.  2s.  td. 

MoUdre.    Les  Fourberies  de  Scapin.    With  Voltaire's  Life  of  Moliere. 

By  Gustave  Masson,  B.A.  .       .         Extra  fcap.  8vo.  stiff  covers,  is.  6d. 

BKnsset.      On   ne  badine  pas  avec  V Amour,  and  Fantasio.     With 

Introduction,  Notes,  etc.,  by  Walter  Merries  Pollock.    Extra  fcap.  8vo.  2s. 


NOVELETTES  :— 

Zavier  de  Maistre.    Voyage  autour  de  ma  Chambre.  \ 
Madame  de  Dnras.     Ourika.  ^7 

Erckmann-Clxatrian.Z^  Vieux  Tailleur.  1 


Alfred  de  Vigrny.      La  Veillee  de  Vincennes.  ^^^,  ^^ 

Edmond  Abont.         LesJu7neauxdeVHdtelCorneille.\is.  td. 
Bodolphe  TopfFer.     Mesaventures  d'un  £colier.        ) 


Gustave 

Masson,  B.A., 

rd     Edition 


Ext.  fcap.  Svo. 
•  1  ; 


Voyage  autour  de  ma  Chavibre,  separately,  limp,  is.  td. 


Perranlt.     Poptilar   Tales.    Edited,  with  an  Introduction  on  Fairy 
Tales,  etc  ,  by  Andrew  Lang,  M.A Extra  fcap.  Svo.  5^.  td. 

Qninet.    Lettres  a  sa  Mire.    Edited  by  G.  Saintsbury,  M.A. 

^  Extra  fcap.  8vo.  2* . 

Bacine.   Esther.   Edited  by  G.  Saintsbury,  M.A.    Extra  fcap.  Svo.  2  j. 

i»anl„«         Andromaaue  )  With    Louis    Racine's    Life   of  his    Father.    By 
Bacine.       Andromaque.  (     Qustave  Masson,  B.A. 


Corneille.  Le  Menteur 

Begnard. 

Brneys  and  Palaprat. 


le. ) 


Le  Joueur.         )  By 
Le  Grondeur.     \ 


Extra  fcap.  Svo.  2s.  td. 

Gustave  Masson,  B.A. 
Extra  fcap.  8vo.  2s.  td. 


12 


CLARENDON  PRESS 


Sainte-Benve.  Selections  from  the  Causeries  du  Lundi.  Edited  by 
G.  Saintsburv,  M.A Extra  fcap.  8vo.  2/. 

Sevign6.  Selections  from  the  Correspondence  ^Madame  de  S6viffn6 
and  her  chief  Contemporaries.  Intended  more  especially  for  Girls'  Schools.  Bv 
GusTAVK  Masson,  B.A Extra  fcap.  8vo.3i. 

Voltaire.  Mh'oj>e.   Edited  byG.  Saintsbury,  M.A.  Extra  fcap.  8vo. 


2S. 


Dante.    Selections  from  the  'Inferno:    With  Introduction  and  Notes, 
by  H.  B.  CoTTERiLL,  B.A Extra  fcap.  Svo.  4J.  6rf. 

Tasso.    La  Gerusalemme  Liberaia.    Cantos  i,  ii.    With  Introduction 
and  Notes,  by  the  same  Editor Extra  fcap.  Svo.  «.  W, 


GERMAN,    GOTHIC,   ICELANDIC,    &o. 

Buchhelm.  Modem  German  Reader,  A  Graduated  Collection  of 
Extracts  m  Prose  and  Poetry  from  Modem  German  writers.  Edited  by  C.  A. 
BucHHEiM,  Phil.  Doc. 

^^^  \   ,^^'^  English  Notes,  a  Grammatical  Appendix,  and  a  complete 
Vocabulary.     Fourth  Edition.  ,        ,        .  Extra  fcap.  Svo.  zs.  6d. 

Part  II.    With  English  Notes  and  an  Index.    Extra  fcap.  Svo.  2*.  6d. 
Part  III.    In  preparation. 

Zixn^e.  The  Germans  at  Home ;  a  Practical  Introduction  to  German 
Conversation,  with  an  Appendix  containing  the  Essentials  of  German  Grammar. 
By  Hermann  Lange.     Tkird  Edition 8vo.  2^.  (>d, 

Iiang-e.  The  German  Manual;  a  German  Grammar,  a  Reading 
Book,  and  a  Handbook  of  German  Conversation.    By  the  same  Author. 

Svo.  7*.  6d. 

Lan^e.  A  Gra?nmar  of  the  German  Language,  being  a  reprint  of  the 
Grammar  contained  in  The  Gertnan  RIanual.  By  the  same  Author.     Svo.  3J.  6d. 

tanffe.  Gerjnan  Composition  ;  a  Theoretical  and  Practical  Guide  to 
V***  Art  of  Translating  English  Prose  iato  German.  By  the  same  Author. 
Second  Editio7t Svo.  4*.  6^. 

lA  Key  in  Preparation.'^ 

Iiang-e.  German  Spelling :  A  Synopsis  of  the  Changes  which  it  has 
undergone  through  the  Government  Regulations  of  1880     .      Paper  cover,  td. 


Becker's    Pnedrlc^    der    Grosse.      With    an    Historical     Sketch 
of  the  Rise  of  Prussia  and  of  the  Times  of  Frederick  the  Great.     With  Man 
Edited  by  C.  A.  Buchheim.  Phil.  Doc.     .        .        .        Extra  fcap.  8vo  3^.  S 

Goethe.     Egmont.     With  a  Life  of  Goethe,  etc.     Edited  by  C    A 
BucHHKiM,  PhU.  Doc.     Third  Edition,         .        .        .         Extra  fcap.  Svi.  3,! 

Goethe.     Iphigenie  ajtf  Tauris.    A  Drama.    With  a  Critical  Intro- 
duction and  Notes.    Edited  by  C.  A.  Buchhkim,  Phil.  Doc.    Second  Edition, 

Extra  fcap.  Svo.  3X. 

Heine's  Harzreise.    With  a  Life  of  Heine,  etc.    Edited  by  C    A 
Buchheim,  Phil.  Doc.  Extra  fcap.  Svo.  stiff  covers,  is.  6d.  cloth,  2J.  (J. 


LIST  OF  SCHOOL  BOOKS, 


13 


Heine's  Prosa,  being  Selections  from  his  Prose  Works.  Edited  with 
English  Notes,  etc.,  by  C.  A.  Buchhkim,  Phil.  Doc.       Extra  fcap.  Svo.  ^s.  6d, 

Iiesslng'.  Laokoon,  With  Introduction,  Notes,  etc.  By  A.  Hamann, 
Phil.  Doc,  M.A Extra  fcap.  Svo.  45.  td. 

Lessingf.  Minna  von  Barnhelm.  A  Comedy.  With  a  Life  of 
Lessing,  Critical  Analysis,  Complete  Commentary,  etc.  Edited  by  C.  A. 
Buchheim,  Phil.  Doc.    Fifth  Edition.     .        .        ,        Extra  fcap.  Svo.  y.  6d. 

Lessing*.  Nathan  der  Weise.  With  English  Notes,  etc.  Edited  by 
C.  A.  Buchheim,  Phil.  Doc.    Second  Edition.        ,       Extra  fcap.  Svo.  4^.  6d. 

Hiebnhr's  Gricchische  Heroen-Geschichten.  Tales  of  Greek  Heroes. 
Edited  with  English  Notes  and  a  Vocabulary,  by  Emma  S.  Buchheim.     • 

Extra  fcap.  Svo.  cloth,  2S. 

Schiller's  Historische  Skizzen: — Egmonts  Leben  und  Tod,  and  Bela- 
gerung  von  Antwerpen.  Edited  by  C.  A.  Buchheim,  Phil.  Doc.  Third 
Edition,  Revised  and  Enlarged^  with  a  Map.  ,        Extra  fcap.  Svo.  2 J.  td. 

Schiller.  Wilhelm  Tell.  With  a  Life  of  Schiller ;  an  Historical  and 
Critical  Introduction,  Arguments,  a  Complete  Commentary,  and  Map.  Edited 
by  C.  A.  Buchheim,  Phil.  Doc.    Sixth  Editioti.      ,       Extra  fcap.  Svo.  3^.6^/. 

Schiller.  Wilhelm  Tell.  Edited  by  C.  A.  Buchheim,  Phil.  Doc. 
School  Edition.    With  Map.  .....  Extra  fcap.  Svo.  2s. 

Schiller.  Wilhelm  Tell,  Translated  into  English  Verse  by  E. 
Massie,  M.A.         . Extra  fcap.  Svo.  5J. 

Schiller.  Die  Jungfrau  von  Orleatis,  Edited  by  C.  A.  Buchheim, 
Phil.  Doc.    [In  preparation. 1 


Scherer.  A  History  of  German  Literature.  By  W.  Scherer. 
Translated  from  the  Third  German  Edition  by  Mrs.  F.  Convbeare.  Edited 
by  F.  Max  Muller.    2  vols. Svo.  21*. 

Max  Miillcr.     The  German  Classics  from  the  Fourth  to  the  Nineteenth 

Century.  With  Biographical  Notices,  Translations  into  Modern  German,  and 
Notes,  by  F.  Max  Muller,  M.A,  A  New  edition,  revised,  enlarged,  and 
adapted  to  Wilhelm  Scherer's  History  oj  Gertnan  Literature^  by  F. 
Lichtenstein.    2  vols Crown  Svo.  2 if. 

Wright.  An  Old  High  Get'man  P^'imer.  With  Grammar,  Notes, 
and  Glossary.     By  Joseph  Wright,  Ph.D.        .       .        Extra  fcap.  Svo.  -^s.  td. 

Wright.  A  Middle  High  German  Primer.  With  Grammar,  Notes, 
and  Glossary.     By  Josefh  Wright,  Ph.  D.     .         .        Extra  fcap.  Svo.  3J.  td. 

Skeat.  The  Gospel  of  St,  Mark  in  Gothic,  Edited  by  W.  W.  Skeat, 
Litt.  D.      .       .        . Extra  fcap.  Svo.  4^. 

Sweet.  An  Icelandic  Primer,  with  Grammar,  Notes,  and  Glossary. 
By  Henry  Sweet,  M.A.     ......        Extra  fcap.  Svo.  3^.  td. 

Viginssoii  and  Powell.  An  Icelandic  Prose  Reader,  with  Notes, 
Grammar,  and  Glossary.  By  Gudbrand  Vigfusson,  M.A.,  and  F.  York 
Powell,  M.A. Extra  fcap.  Svo.  lof.  td. 


14 


CLARENDON  PRESS 


MATHEMATICS  AND  PHYSICAL  SCIENCE. 

^^^.?'o  ^  ^^^^  ^^^^  of  Algebra  {with  Answers  to  the  ExampksX     By 
W.  Steadman  Aldis,  M.A Crown  Svo:  7^.  ei. 

Hamilton  and  BaU.    Book-keeping,    By  Sir  R.  G.  C.  Hamilton, 

5' /•    •'l"/rvi°"''  ^"^^^  ^°^  '^*  ^"^  °^  Q""'^'"'  Ball.  &  Co.).     New  and 
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Hensley.  Figures  made  Easy :  a  first  Arithmetic  Book.  By  Lewis 
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Hensley.     The  Scholar's  Arithmetic,    By  the  same  Anthor. 

Crown  8vo.  2J.  dd. 

Hensley.     Answers  to  the  Examples  in   the  Scholar's  Arithmetic, 

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Hensley.     The  Scholar's  Algebra,    An  Introductory  work  on  Algebra 
By  the  same  Author Crown  8vo.  2^.  6^. 


Baynes.     Lessons  on   Thermodynamics,      By  R.  E.  Baynes    M  A 
Lee's  Reader  in  Physics Crown  8vo.  71.*  6^?. 

Donkln.    Acoustics.  By  W.  F.  DoNKiN,  M.  A.,  F.R.S.    Second  Edition, 

^___ Crown  8vo.  7*.  6d, 

BucUd  Bevlsed.    Containing  the  essentials  of  the  Elements  of  Plane 
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EucUd.     Geometry  in  Space.     Containing  parts  of  Euclid's  Eleventh 
and  Twelfth  Books.     By  the  same  Editor.         .        .        .        Crown  8vo.  35.  6ar. 

Harconrt  and  Madan.    Exercises  in  Practical  Chemistry,     Vol  I 
Elementary  Exercises.    By  A.  G.  Vernon  Harcourt,  M.A. :  and  H.G* 
Madan,  M.A.    Fourth  Edition,    Revised  by  H.  G.  Madan,  M.A. 

Crown  8vo.  lox.  td, 

Madan.     Tables  of  Qualitative  Analysis,   Arranged  by  H.  G.  Madan 
^"^ Large  4to.  4J.  (J. 

Maxwell.  An  Elementary  Treatise  on  Electricity,  By  J  Clerk 
Maxwell,  M.A.,  F.R.S.    Edited  by  W.  Garnett,  M.A.      Demy  8*vo.  ^s.  6d, 

Stewart.  A  Treatise  on  Heat,  with  numerous  Woodcuts  and  Dia- 
pams.  By  Balfour  Stewart,  LL.D.,  F.R.S.,  Professor  of  Natural  Philosophy 
in  Owens  CoUege,  Manchester.    Fifth  Edition,         .     Extra  fcap.  8vo  ^s  (J 


LIST  OF  SCHOOL  BOOKS, 


15 


Williamson.  Chemistry  for  Students,  By  A.  W.  Williamson, 
Phil.  Doc,  F.R.S.,  Professor  of  Chemistry,  University  College  London.  A  new 
Edition  with  Solutions ,        Extra  fcap.  8vo.  8j.  bd. 


Com'blnation  Chemical  Labels.    In  two  Parts,  gummed  ready  for  use. 
Part  I,  Basic  Radicles  and  Names  of  Elements.     Part  II,  Acid  Radicles. 

Price  3*.  (>d. 


HISTORY,    POLITICAL    ECONOMY, 
GEOGRAPHY,   &c. 

Danson.    The  Wealth  of  Households.    By  J.  T.  Danson.    Cr.  8vo.  5J. 

Freeman.  A  Short  History  of  the  Norman  Conquest  of  England, 
By  E.  A,  Freeman,  M.A.    Second  Edition,  ,  Extra  fcap.  8vo.  2j.  (td, 

Oeorg'e.  Genealogical  Tables  illustrative  of  Modern  History.  By 
H.  B.  George,  M.A.     Third  Edition,  Revised  and  Enlarged.     Small  4to.  12s, 

Hug'lies  (Alfred).  Geography  for  Schools,  Part  I,  Practical  Geography. 
With  Diagrams Extra  fcap.  8vo.  2^,  td. 

ZitoUn.  A  History  of  France.  With  Numerous  Maps,  Plans,  and 
Tables.    By  G.  W.  Kitchin,  D.D.,  Dean  of  Winchester.    Second  Edition. 

Vol.  I.  To  1453.     Vol.  II.  1453-1624.    Vol.  III.  1624-1793.    each  los.  6d. 

Lucas.  Introduction  to  a  Historical  Geography  of  the  British  Colonies. 
By  C.  P.  Lucas,  B.A.  ....        Crown  Svo.,  with  8  maps,  4J.  dd. 

Bawlinson.  A  Manual  of  Ancient  History.  By  G.  Rawlinson, 
M.A.,  Camden  Professor  of  Ancient  History.  Second  Edition,     Demy  8vo.  14J. 

Bogfers.  A  Manual  of  Political  Economy,  for  the  use  of  Schools. 
By  J.  E.  Thorold  Rogers,  M.A.    Third  Edition,       Extra  fcap.  8vo.  4*.  6</. 

Stnbbs.  The  Constitutional  History  of  England,  in  its  Origin  and 
Development,  By  William  Stubbs,  D.D.,  Lord  Bishop  of  Chester.  Three 
vols. Crown  Svo.  each  12X. 

Stubbs.    Select  Charters  and  other  Illustrations  of  English   Con- 

stitutional  History,  from  the  Earliest  Times  to  the   Reign   of  Edward   I. 
Arranged  and  edited  by  W.  Stubbs,  D.D.  Fourth  Edition,    Crown  8vo.  8j.  6^. 


Stubbs.    Magna  Carta :  a  careful  reprint. 


.    4to.  stitched,  is. 


ART. 

HuUah.     The  Cultivation  of  the  Speaking  Voice,    By  John  Hullah. 

Extra  fcap.  Svo.  2 J.  6d, 

Maclaren.  A  System  of  Physical  Education :  Theoretical  and  Prac- 
tical, With  346  Illustrations  drawn  by  A.  Macdonald,  of  the  Oxford  School  of 
Art.    By  Archibald  Maclaren,  the  Gymnasium,  Oxford.    Second  Edition. 

Extra  fcap.  8vo.  ^s,  td. 


1 6       CLARENDON  PRESS  LIST  OF  SCHOOL  BOOKS. 


Troutbeck  and  Dale.     A  Music  Primer  for  Schools.     By  T  Trout- 

M  T' B  M;;/Tr^r^"'^*^  ^r^'  in  Westminster  Schoo  ,  and  £f  D.^I 
M.A.,  B.  Mus..  late  Assistant  Master  in  Westminster  School.  Crown  Svo.'wlS 

Tyrwhltt.    A  Handbook  of  Pictorial  Art.     By  R.  St  T  Tvrwmttt 

ut»M^/».       ,        ,        ,         avo.  half  morocco^  i8f , 

Upcott.    ^«  Introduction  to  Greek  Sculpture,    By  L.  E.  Upcott, 
Crown  8vo.  4J.  6</. 


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Helps  to  the  Study  of  tlie  Bible,  taken  from  the  Oxford  Bible  for 

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SellnH,^      .t     "''"1"'  of  Scripture  History  and  the  Characteristics  7f 
Bible  Lands  ;  with  a  complete  Index  of  Subjects,  a  Concordance,  a  Dictionary 
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